ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present composite 3.6 and 4.5 micron luminosity functions for cluster galaxies measured from the Spitzer Deep, Wide-Field Survey (SDWFS) for 0.3<z<2. We compare the evolution of m* for these luminosity functions to models for passively evolving stellar populations to constrain the primary epoch of star formation in massive cluster galaxies. At low redshifts (z < 1.3) our results agree well with models with no mass assembly and passively evolving stellar populations with a luminosity-weighted mean formation redshift zf=2.4 assuming a Kroupa initial mass function (IMF). We conduct a thorough investigation of systematic biases that might influence our results, and estimate systematic uncertainites of Delta zf=(+0.16-0.18) (model normalization), Delta zf=(+0.40-0.05) (alpha), and Delta zf=(+0.30-0.45) (choice of stellar population model). For a Salpeter type IMF, the typical formation epoch is thus strongly constrained to be z ~2-3. Higher formation redshifts can only be made consistent with the data if one permits an evolving IMF that is bottom-light at high redshift, as suggested by van Dokkum et al 2008. At high redshift (z > 1.3) we also witness a statistically significant (>5sigma) disagreement between the measured luminosity function and the continuation of the passive evolution model from lower redshifts. After considering potential systematic biases that might influence our highest redshift data points, we interpret the observed deviation as potential evidence for ongoing mass assembly at this epoch.
We discuss novel features of a new continuum RPA formulated in the coordinate-space Hartree-Fock-Bogoliubov framework. This continuum quasiparticle RPA takes into account both the one- and two-particle escaping channels. The theory is tested with numerical calculations for monopole, dipole and quadrupole excitations in neutron-rich oxygen isotopes near the drip-line. Effects of the particle-particle RPA correlation caused by the pairing interaction are discussed in detail, and importance of the selfconsistent treatment is emphasized.
We present a new method to marginalize over uncertainties in redshift distributions, $N(z)$, within tomographic cosmological analyses applicable to current and upcoming photometric galaxy surveys. We allow for arbitrary deviations from the best-guess $N(z)$ governed by a general covariance matrix describing the uncertainty in our knowledge of redshift distributions. In principle, this is marginalization over hundreds or thousands of new parameters describing potential deviations as a function of redshift and tomographic bin. However, by linearly expanding the theory predictions around a fiducial model, this marginalization can be performed analytically, resulting in a modified data covariance matrix that effectively downweights the modes of the data vector that are more sensitive to redshift distribution variations. We showcase this method by applying it to the galaxy clustering measurements from the Hyper Suprime-Cam first data release. We illustrate how to marginalize over sample-variance of the calibration sample and a large general systematic uncertainty in photometric estimation methods, and explore the impact of priors imposing smoothness in the redshift distributions.
We examine the renormalization of the first order formulation of Yang-Mills theory, by using the BRST idenities. These preserve the gauge invariance of the theory and enable a recursive proof of renormalizability to higher orders in perturbation theory. The renormalization involves non-linear mixings as well as re-scalings of the fields and sources, which lead to a renormalized action at all orders.
Previously proposed procedure for improving the effective potential by using renormalization group equation (RGE) is generalized so as to be applicable to any system containing several different mass scales. If one knows L-loop effective potential and (L+1)-loop RGE coefficient functions, this procedure gives an improved potential which satisfies the RGE and contains all of the leading, next-to-leading,..., and L-th-to-leading log terms. Our procedure here also clarifies how naturally the so-called effective field theory can be incorporated in the RGE in MS bar scheme.
In this paper, we investigate the properties of well-rounded twists of a given ideal lattice of an imaginary quadratic field $K$. We show that every ideal lattice $I$ of $K$ has at least one well-rounded twist lattice. Moreover, we provide an explicit algorithm to compute all well-rounded twists of $I$.
We introduce a new approach to obtaining pointwise estimates for solutions of elliptic boundary value problems when the operator being considered satisfies a certain type of weighted integral inequalities. The method is illustrated on several examples, including a scalar second-order elliptic equation, the 3D Lam\'{e} system, and a scalar higher-order elliptic equation. The techniques can be extended to other elliptic boundary value problems provided that the corresponding weighted integral inequalities are satisfied.
We study smooth threefolds of the projective space of dimension 5 whose quadrisecant lines don't fill up the space. We give a complete classification of those threefolds X whose only quadrisecant lines are the lines contained in X. Then we prove that, if X admits "true" quadrisecant lines, but they don't fill up the space, then either X is contained in a cubic hypersurface, or it contains a family of dimension at least two of plane curves of degree at least four.
In the present work we introduce a generalized lattice-gas model to study the multilayer adsorption of interacting polyatomics on heterogeneous surfaces. Using an approximation in the spirit of the well-known Brunauer--Emmet--Teller (BET) model, a new theoretical isotherm is obtained in one- and two-dimensional lattices and compared with Monte Carlo simulation. In addition, we use the BET approach to analyze these isotherms and to estimate the monolayer volume. In all cases, we found that the use of the BET equation leads to an underestimate of the true monolayer capacity. However, significant compensation effects were observed for heterogeneous surfaces and attractive lateral interactions.
Wasserstein distances provide a metric on a space of probability measures. We consider the space $\Omega$ of all probability measures on the finite set $\chi = \{1, \dots ,n\}$ where $n$ is a positive integer. 1-Wasserstein distance, $W_1(\mu,\nu)$ is a function from $\Omega \times \Omega$ to $[0,\infty)$. This paper derives closed form expressions for the First and Second moment of $W_1$ on $\Omega \times \Omega$ assuming a uniform distribution on $\Omega \times \Omega$.
The J1-J2 model on a square lattice exhibits a rich variety of different forms of magnetic order that depend sensitively on the ratio of exchange constants J2/J1. We use bulk magnetometry and polarized neutron scattering to determine J1 and J2 unambiguously for two materials in a new family of vanadium phosphates, Pb2VO(PO4)2 and SrZnVO(PO4)2, and we find that they have ferromagnetic J1. The ordered moment in the collinear antiferromagnetic ground state is reduced, and the diffuse magnetic scattering is enhanced, as the predicted bond-nematic region of the phase diagram is approached.
Efforts to detect a primordial $B$-mode of CMB polarization generated by inflationary gravitational waves ought to mitigate the large variance associated with the $B$-modes produced by gravitational lensing, a process known as delensing. A popular approach to delensing entails building a lensing $B$-mode template by mimicking the lensing operation, either at gradient order or non-perturbatively, using high-resolution $E$-mode observations and some proxy of the lensing potential. By explicitly calculating all contributions to two-loop order in lensing to the power spectrum of $B$-modes delensed with such a template in the noise-free limit, we are able to show that: (i) corrections to the leading-order calculation of the lensing $B$-mode power spectrum only enter at the $O(1)\,\%$ level because of extensive cancellations between large terms at next-to-leading order; (ii) these cancellations would disappear if a gradient-order template were to be built from unlensed or delensed $E$-modes, giving rise to a residual delensing floor of $O(10)\,\%$ of the original power; (iii) new cancellations arise when the lensed $E$-modes are used in the gradient-order template, allowing for the delensing floor to be as low as $O(1)\,\%$ of the original power in practical applications of this method; and (iv) these new cancellations would disappear for a non-perturbative template constructed from the lensed $E$-modes, reintroducing a residual delensing floor of $O(10)\,\%$. We further show that the gradient-order template outperforms the non-perturbative one in realistic scenarios with noisy estimates of the $E$-mode polarization and lensing potential. We therefore recommend that in practical applications of $B$-mode template delensing, where the template is constructed directly from the (filtered) observed $E$-modes, the gradient-order approach should be used rather than a non-perturbative remapping.
For any prime number $p$ and field $k$, we characterize the $p$-retract rationality of an algebraic $k$-torus in terms of its character lattice. We show that a $k$-torus is retract rational if and only if it is $p$-retract rational for every prime $p$, and that the Noether problem for retract rationality for a group of multiplicative type $G$ has an affirmative answer for $G$ if and only if the Noether problem for $p$-retract rationality for $G$ have a positive answer for all $p$. For every finite set of primes $S$ we give examples of tori that are $p$-retract rational if and only if $p\notin S$.
Near infrared (IR) studies of Cepheid variables in the LMC take advantage of the reduced light curve amplitude and metallicity dependence at these wavelengths. This work presents such photometry for two young clusters known to contain sizeable Cepheid populations: NGC 1866 and NGC 2031. Our goal is to determine light curves and period-luminosity (PL) relations in the near-IR, to assess the similarity between cluster and field pulsators, and to examine the predictive capability of current pulsation models. The light curves are obtained from multiwavelength broadband J,H,Ks photometry of Cepheids in both clusters, with periods previously established from optical photometry. Mean magnitudes for the Cepheids are used to construct PL relations in the near-IR. The properties in the PL planes are compared with the behavior of field Cepheids in the LMC and with the predictions of recent pulsational models, both canonical and overluminous. Cluster and field Cepheids are homogeneous and the inclusion of the cluster Cepheids in the field sample extends nicely the PL relation. The slope of the PL relation is constant over the whole period range and does not show -- at least in the adopted IR bands -- the break in slope at P ~ 10 d reported by some authors. A comparison with the predictions of pulsation models allows an estimate for the distance moduli of NGC 1866 and NGC 2031. The two clusters are found to lie at essentially the same distance. Fitting of theoretical models to the data gives, for the K filter, (m-M)_0 = 18.62+-0.10 if canonical models are used and (m-M)_0 = 18.42+-0.10 if overluminous models are used. On the basis of this result, some considerations on the relationship between the clusters and the internal structure of the LMC are presented.
In this paper we prove a functional limit theorem for the weighted profile of a $b$-ary tree. For the proof we use classical martingales connected to branching Markov processes and a generalized version of the profile-polynomial martingale. By embedding, choosing weights and a branch factor in a right way, we finally rediscover the profiles of some well-known discrete time trees.
Naturals and synthetic perovskites are widely used functional materials thanks to their particular physical properties, such as superconductivity, ferroelectricity and photo-activity. Many of these properties are related to static or dynamic motion of octahedral units; Yet a full understanding of the relationships between perovskite crystal structure, chemical bonding and physical properties is currently missing. Several studies indicate the existence of dynamic disorder generated by anharmonic motion of octahedral units e.g. in halide perovskite structures. In this work, we derive all possible space groups for simple perovskites $\rm ABX_3$ with dynamical octahedral tilting. The derived space groups extend the well established space group tables for static tiltings by [Glazer, A. Acta Cryst. B 1972, 28, 3384-3392; Aleksandrov, K. Ferroelectrics 1976, 24, 801-805; Howard, C.J., Stokes, H.T. Acta Cryst. B 1998, 54, 782-789]. We demonstrate ubiquity of dynamical tilting by analysing the structural data for perovskites reported in recent scientific publications and discuss the signature of dynamic tilting in the corresponding structures. Finally, we discuss the possible influence of dynamic disorder on the physical properties of halide perovskites.
A generalisation of Price's theorem is given for application to Inflationary Cosmologies. Namely, we show that on a Schwarzschild--de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.
This note shows that under $(p,\alpha, N)\in (1,\infty)\times(0,2)\times\mathbb Z_+$ the fractional order differential inequality $$ (\dagger)\quad u^p \le (-\Delta)^{\frac{\alpha}{2}} u\quad\hbox{in}\quad\mathbb R^{N} $$ has the property that if $N\le\alpha$ then a nonnegative solution to $(\dagger)$ is unique, and if $N>\alpha$ then the uniqueness of a nonnegative weak solution to $(\dagger)$ occurs when and only when $p\le N/(N-\alpha)$, thereby innovatively generalizing Gidas-Spruck's result for $u^p+\Delta u\le 0$ in $\R^N$ discovered in \cite{GS}.
We theoretically investigate the nonlinear optical pulse responses of excitons in a thin film where the excitonic center-of-mass motion is confined. A large interaction volume between excitons and radiation yields particular coupled states with radiative decay times reaching several femto-seconds. By considering two polarization directions of light, we reveal that these fast-decay modes dominantly survive in an optical Kerr spectra even under a massive nonradiative damping $\Gamma=30$ meV. The results clearly show that there is an optimal combination of the incident pulse width and the film thickness for maximizing the integrated intensity of nonlinear signals.
Let $\Gamma\backslash\mathbb H^3$ be a finite-volume quotient of the upper-half space, where $\Gamma\subset {\rm SL}(2,\mathbb C)$ is a discrete subgroup. To a finite dimensional unitary representation $\chi$ of $\Gamma$ one associates the Selberg zeta function $Z(s;\Gamma;\chi)$. In this paper we prove the Artin formalism for the Selberg zeta function. Namely, if $\tilde\Gamma$ is a finite index group extension of $\Gamma$ in ${\rm SL}(2,\mathbb C)$, and $\pi={\rm Ind}_{\Gamma}^{\tilde\Gamma}\chi$ is the induced representation, then $Z(s;\Gamma;\chi)=Z(s;\tilde\Gamma;\pi)$. In the second part of the paper we prove by a direct method the analogous identity for the scattering function, namely $\phi(s;\Gamma;\chi)=\phi(s;\tilde\Gamma;\pi)$, for an appropriate normalization of the Eisenstein series.
We examine the Newtonian potential in gravitational cohomology. This is given by a symmetric, two-index tensor field, which satisfies the wave equation in empty space. Furthermore, the associated gravitational field strength, obtained by applying the coboundary operator to the potential, is constructed for the case of a stationary point mass and shown to give the classical result.
A tight relation between the size of the broad-line region (BLR) and optical luminosity has been established in about 50 active galactic nuclei studied through reverberation mapping of the broad Hbeta emission line. The R_blr-L relation arises from simple photoionization considerations. Using a general relativistic model of an optically thick, geometrically thin accretion disk, we show that the ionizing luminosity jointly depends on black hole mass, accretion rate, and spin. The non-monotonic relation between the ionizing and optical luminosity gives rise to a complicated relation between the BLR size and the optical luminosity. We show that the reverberation lag of Hbeta to the varying continuum depends very sensitively to black hole spin. For retrograde spins, the disk is so cold that there is a deficit of ionizing photons in the BLR, resulting in shrinkage of the hydrogen ionization front with increasing optical luminosity, and hence shortened Hbeta lags. This effect is specially striking for luminous quasars undergoing retrograde accretion, manifesting in strong deviations from the canonical R_blr-L relation. This could lead to a method to estimate black hole spins of quasars and to study their cosmic evolution. At the same time, the small scatter of the observed R_blr-L relation for the current sample of reverberation-mapped active galaxies implies that the majority of these sources have rapidly spinning black holes.
We study solvability of the Diophantine equation \begin{equation*} \frac{n}{2^{n}}=\sum_{i=1}^{k}\frac{a_{i}}{2^{a_{i}}}, \end{equation*} in integers $n, k, a_{1},\ldots, a_{k}$ satisfying the conditions $k\geq 2$ and $a_{i}<a_{i+1}$ for $i=1,\ldots,k-1$. The above Diophantine equation (of polynomial-exponential type) was mentioned in the monograph of Erd\H{o}s and Graham, where several questions were stated. Some of these questions were already answered by Borwein and Loring. We extend their work and investigate other aspects of Erd\H{o}s and Graham equation. First of all, we obtain the upper bound for the value $a_{k}$ given in terms of $k$ only. This mean, that with fixed $k$ our equation has only finitely many solutions in $n, a_{1},\ldots, a_{k}$. Moreover, we construct an infinite set $\cal{K}$, such that for each $k\in\cal{K}$, the considered equation has at least five solutions. As an application of our findings we enumerate all solutions of the equation for $k\leq 8$. Moreover, by applying greedy algorithm, we extend Borwein and Loring calculations and check that for each $n\leq 10^4$ there is a value of $k$ such that the considered equation has a solution in integers $n+1=a_{1}<a_{2}<\ldots <a_{k}$. Based on our numerical calculations we formulate some further questions and conjectures.
We predict the possibility to generate a finite stationary spin current by applying an unbiased ac driving to a quasi-one-dimensional asymmetric periodic structure with Rashba spin-orbit interaction and strong dissipation. We show that under a finite coupling strength between the orbital degrees of freedom the electron dynamics at low temperatures exhibits a pure spin ratchet behavior, {\it i.e.} a finite spin current and the absence of charge transport in spatially asymmetric structures. It is also found that the equilibrium spin currents are not destroyed by the presence of strong dissipation.
Dark Matter in Earth intersecting orbits can scatter off the electrons and lose energy, and finally be gravitationally bound to Earth. Eventually they lose enough energy and accumulate at the core. It is assumed that DM annihilates/decays predominantly into Standard Model particles inside Earth. The heat flux from these processes is compared with the experimentally measured value of internal heat flux of Earth which is 44 TW. Assuming steady state between capture and annihilation/decay, we put constraints on the scattering cross section of DM with electrons as a function of their mass. For low mass regions ($<10^{-2}$GeV), these constraints on leptophilic DM are better than ones obtained from direct-detection experiments.
We demonstrate the predicted out-of-plane precession induced by spin transfer in magnetic nanostructures with in-plane magnetic field. We show that other magnetic excitations have a significant effect on the stability of the out-of plane precession, making it extremely sensitive to the orientation of the applied magnetic field. The data are supported with micromagnetic simulations. Our results elucidate the relation between the excitation spectrum and the specific dynamical behaviors of nanoscale magnets.
Nonequilibrium phase transition properties of a mixed Ising ferrimagnetic model consisting of spin-1/2 and spin-3/2 on a square lattice under the existence of a time dependent oscillating magnetic field have been investigated by making use of Monte Carlo simulations with single-spin flip Metropolis algorithm. A complete picture of dynamic phase boundary and magnetization profiles have been illustrated and the conditions of a dynamic compensation behavior have been discussed in detail. According to our simulation results, the considered system does not point out a dynamic compensation behavior, when it only includes the nearest-neighbor interaction, single-ion anisotropy and an oscillating magnetic field source. As the next-nearest-neighbor interaction between the spins-1/2 takes into account and exceeds a characteristic value which sensitively depends upon values of single-ion anisotropy and only of amplitude of external magnetic field, a dynamic compensation behavior occurs in the system. Finally, it is reported that it has not been found any evidence of dynamically first-order phase transition between dynamically ordered and disordered phases, which conflicts with the recently published molecular field investigation, for a wide range of selected system parameters.
Using Monte Carlo Simulations (MCS), based the Metropolis algorithm, we examine in this study, the magnetic properties of the rare earth based compound GdN. In a first step, we discuss and study the ground state phase diagrams explored in the different planes of physical parameter. The obtained stable configurations are illustrated by comparing the energies modeled by the Hamiltonian of Eq. (1). For non-null temperature values, we present and discuss the behavior the total magnetizations and susceptibilities as a function of: the temperature, the crystal field, the exchange coupling interactions and the external magnetic field. The hysteresis loops are illustrated and analyzed when varying the external magnetic field for specific values of the physical parameters: the temperature, the crystal field and the exchange coupling interactions. In order to complete this study, we present the obtained values of the critical exponents corresponding to compound GdN. Such results have been compared with those existing in the literature.