ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present nine color CCD intermediate-band spectrophotometry of a two square degree field centered on the old open cluster M67, from 3890$\rm \AA$ to nearly 1$\mu$. These observations are taken as a part of the BATC (Beijing-Arizona-Taipei-Connecticut) Color Survey of the Sky, for both scientific and calibration reasons. With these data we show that the BATC survey can reach its goal of obtaining spectrophotometry to a zero point accuracy of 0.01 mag, and down to V = 21 with 0.3 mag random error. We fit the color-magnitude diagrams (CMDs) with Worthey's theoretical models. The net result is the excellent fit of the 4.0 Gyr, [Fe/H] = $-0.10$ model to our data, including a good fit to the main sequence (MS) turn-off. Our data are consistent with a toy model with 50\% of the stars in M67 being binaries and a random distribution of binary mass-ratios, although other models with different mass-ratio distributions cannot be ruled out. The spatial distribution and mass function (MF) of stars in M67 show marked effects of dynamical evolution and evaporation of stars from the cluster. Blue stragglers and binary stars are the most condensed within the cluster, with degree of condensation depending on mass.We find M67 to have an elongated shape, oriented at an angle of $15^{\circ}$ relative to the galactic plane. Within its tidal radius, the observed MF of M67 between 1.2 $\rm M_\odot$ and $\rm 0.8 M_\odot$ has a Salpeter slope $\rm \eta = -1.93 \pm 0.66$. For stars of mass below 0.8 $\rm M_\odot$, $\rm \eta \sim 0$. It is plausible that the leveling-off of the MF at lower masses is a result of evaporation of lower mass stars in this mass range at a rate of one every $\sim 10^7$ years. If so, it is plausible that the IMF of M67 has the canonical field value of $\rm \eta = -2.0$.
We investigate coupled spin and heat transport in easy-plane magnetic insulators. These materials display a continuous phase transition between normal and condensate states that is controlled by an external magnetic field. Using hydrodynamic equations supplemented by Gross-Pitaevski phenomenology and magnetoelectric circuit theory, we derive a two-fluid model to describe the dynamics of thermal and condensed magnons, and the appropriate boundary conditions in a hybrid normal-metal|magnetic-insulator|normal-metal heterostructure. We discuss how the emergent spin superfluidity can be experimentally probed via a spin Seebeck effect measurement.
Within a superfield approach, we formulate a simple quantum generating equation of the field - antifield formalism. Then, we derive the Schroedinger equation with the Hamiltonian whose $\Delta$ - exact part serves as a generator to the quantum master-transformations. We show that these generators do satisfy a nice composition law in terms of the quantum antibrackets. We also present an $Sp(2)$ symmetric extension as to the main construction, with specific features caused with the principal fact that all basic equations become $Sp(2)$ vector valued ones.
Let T be a general complex tensor of format $(n_1,...,n_d)$. When the fraction $\prod_in_i/[1+\sum_i(n_i-1)]$ is an integer, and a natural inequality (called balancedness) is satisfied, it is expected that T has finitely many minimal decomposition as a sum of decomposable tensors. We show how homotopy techniques allow us to find all the decompositions of T, starting from a given one. Computationally, this gives a guess regarding the total number of such decompositions. This guess matches exactly with all cases previously known, and predicts several unknown cases. Some surprising experiments yielded two new cases of generic identifiability: formats (3,4,5) and (2,2,2,3) which have a unique decomposition as the sum of 6 and 4 decomposable tensors, respectively. We conjecture that these two cases together with the classically known matrix pencils are the only cases where generic identifiability holds, i.e., the only identifiable cases. Building on the computational experiments, we use algebraic geometry to prove these two new cases are indeed generically identifiable.
The advance of image editing techniques allows users to create artistic works, but the manipulated regions may be incompatible with the background. Localizing the inharmonious region is an appealing yet challenging task. Realizing that this task requires effective aggregation of multi-scale contextual information and suppression of redundant information, we design novel Bi-directional Feature Integration (BFI) block and Global-context Guided Decoder (GGD) block to fuse multi-scale features in the encoder and decoder respectively. We also employ Mask-guided Dual Attention (MDA) block between the encoder and decoder to suppress the redundant information. Experiments on the image harmonization dataset demonstrate that our method achieves competitive performance for inharmonious region localization. The source code is available at https://github.com/bcmi/DIRL.
Two proofs of the Koml\'os-Major-Tusn\'ady embedding theorems, one for the uniform empirical process and one for the simple symmetric random walk, are given. More precisely, what are proved are the univariate coupling results needed in the proofs, such as Tusn\'{a}dy's lemma. These proofs are modifications of existing proof architectures, one combinatorial (the original proof with many modifications, due to Cs\"{o}rg\~o, R\'{e}v\'{e}sz, Bretagnolle, Massart, Dudley, Carter, Pollard etc.) and one analytical (due to Sourav Chatterjee). There is one common idea to both proofs: we compare binomial and hypergeometric distributions among themselves, rather than with the Gaussian distribution. In the combinatorial approach, this involves comparing Binomial(n,1/2) distribution with the Binomial(4n,1/2) distribution, which mainly involves comparison between the corresponding binomial coefficients. In the analytical approach, this reduces Chatterjee's method to coupling nearest neighbour Markov chains on integers so that they stay close.
This article offers a detailed analysis of pseudo-phase transitions of Ising and Baxter-Wu models in two-dimensional finite-size lattices. We carry out Wang Landau sampling to obtain the density of states. Using microcanonical inflection point analysis with microcanonical entropy, we obtain the order of the psuedo-phase transitions in the models. The microcanonical analysis results of the second-order transition for the Ising model and the first-order transition for the Baxter-Wu model are consistent with the traditional canonical results. In addition, the third-order transitions are found in both models, implying the universality of higher-order phase transitions.
We present an exact Quantum Monte Carlo study of the attractive 1-dimensional Hubbard model with imbalanced fermion population. The pair-pair correlation function, which decays monotonically in the absence of polarization P, develops oscillations when P is nonzero, characteristic of Fulde-Ferrell-Larkin-Ovchinnikov phase. The pair momentum distribution peaks at a momentum equal to the difference in the Fermi momenta. At strong coupling, the minority and majority momentum distributions are shown to be deformed, reflecting the presence of the other species, and its Fermi surface. The FFLO oscillations survive the presence of a confining potential, and the local polarization at the trap center exhibits a marked dip, similar to that observed experimentally.
Using exact diagonalization (ED) and linear spin wave theory (LSWT) we study the influence of frustration and quantum fluctuations on the magnetic ordering in the ground state of the spin-1/2 J1-J2 Heisenberg antiferromagnet (J1-J2 model) on the body-centered cubic (bcc) lattice. Contrary to the J1-J2 model on the square lattice, we find for the bcc lattice that frustration and quantum fluctuations do not lead to a quantum disordered phase for strong frustration. The results of both approaches (ED, LSWT) suggest a first order transition at J2/J1 $\approx$ 0.7 from the two-sublattice Neel phase at low J2 to a collinear phase at large J2.
This is Part 2 of our work aimed at classifying the long-time behavior of the solution to a free boundary problem with monostable reaction term in space-time periodic media. In Part 1 (see \cite{ddl}) we have established a theory on the existence and uniqueness of solutions to this free boundary problem with continuous initial functions, as well as a spreading-vanishing dichotomy. We are now able to develop the methods of Weinberger \cite{w1, w2} and others \cite{fyz,lyz,lz1,lz2,lui} to prove the existence of asymptotic spreading speed when spreading happens, without knowing a priori the existence of the corresponding semi-wave solutions of the free boundary problem. This is a completely different approach from earlier works on the free boundary model, where the spreading speed is determined by firstly showing the existence of a corresponding semi-wave. Such a semi-wave appears difficult to obtain by the earlier approaches in the case of space-time periodic media considered in our work here.
By using broadband linear and nonlinear dielectric spectroscopy we studied the magnetoelectric dynamics in the chiral antiferromagnet MnWO4. In the multiferroic phase the dielectric response is dominated by the dynamics of domains and domain walls which is strongly dependent on the stimulating electric field. The mean switching time reaches values in the minute range in the middle of the multiferroic temperature regime at T=10 K but unexpectedly decays again on approaching the lower, first-order phase boundary at T_N1=7.6K. The switchability of the ferroelectric domains denotes a pinning-induced threshold and can be described considering a growth-limited scenario with an effective growth dimension of d=1.8. The rise of the effective dynamical coercive field on cooling below the TN2 is much stronger compared to the usual ferroelectrics and can be described by a power law E_c ~{\nu}^1/2. The latter questions the feasibility of fast-switching devices based on this type of material.
For a projective nonsingular curve of genus $g$, the Brill-Noether locus $W^r_d(C)$ parametrizes line bundles of degree $d$ over $C$ with at least $r+1$ sections. When the curve is generic and the Brill-Noether number $\rho(g,r,d)$ equals $1$, one can then talk of the \emph{Brill-Noether curve}. In this paper, we explore the first two invariants of this curve, giving a new way of calculating the genus of this curve and computing its gonality when $C$ has genus 5.
Through comprehensive density functional calculations, the crystallographic, magnetic and electronic properties of $Na_xCoO_2$ ($x$ = 1, 0.875, 0.75, 0.625 and 0.50) were investigated. We found that all Na ions in $NaCoO_2$ and $Na_{0.875}CoO_2$ share the basal coordinates with O ions. However, as $x$ decreases, some of Na ions move within the basal plane in order to reduce the in-plane Na$-$Na electrostatic repulsion. Magnetically, there was strong tendency for type A antiferromagnetism in the $Na_{0.75}CoO_2$ system, while all other Na deficient systems had a weaker ferromagnetic tendency. The results on magnetism were in excellent agreement with the experiments.
We give constraints on the existence of $(\chi,b)$-factors in the global $A$-parameter of a genuine cuspidal automorphic representation $\sigma$ of a metaplectic group in terms of the invariant, lowest occurrence index, of theta lifts to odd orthogonal groups. We also give a refined result that relates the invariant, first occurrence index, to non-vanishing of period integrals of residues of Eisenstein series associated to the cuspidal datum $\chi\otimes\sigma$. This complements our previous results for symplectic groups.
The LHC, with its seven-fold increase in energy over the Tevatron, is capable of probing regions of SUSY parameter space exhibiting qualitatively new collider phenomenology. Here we investigate one such region in which first generation squarks are very heavy compared to the other superpartners. We find that the production of these squarks, which is dominantly associative, only becomes rate-limited at mSquark > 4(5) TeV for L~10(100) fb-1. However, discovery of this scenario is complicated because heavy squarks decay primarily into a jet and boosted gluino, yielding a dijet-like topology with missing energy (MET) pointing along the direction of the second hardest jet. The result is that many signal events are removed by standard jet/MET anti-alignment cuts designed to guard against jet mismeasurement errors. We suggest replacing these anti-alignment cuts with a measurement of jet substructure that can significantly extend the reach of this channel while still removing much of the background. We study a selection of benchmark points in detail, demonstrating that mSquark= 4(5) TeV first generation squarks can be discovered at the LHC with L~10(100)fb-1.
We consider the analogue of the quantum unique ergodicity conjecture for holomorphic Hecke eigenforms on compact arithmetic hyperbolic surfaces. We show that this conjecture follows from nontrivial bounds for Hecke eigenvalues summed over quadratic progressions. Our reduction provides an analogue for the compact case of a criterion established by Luo--Sarnak for the case of the non-compact modular surface. The novelty is that known proofs of such criteria have depended crucially upon Fourier expansions, which are not available in the compact case. Unconditionally, we establish a twisted variant of the Holowinsky--Soundararajan theorem involving restrictions of normalized Hilbert modular forms arising via base change.
The thermodynamical cluster model is known to present a first-order liquid-gas phase transition in the idealized case of an uncharged, infinitely extended medium. However, in most practical applications of this model, the system is finite and charged. In this paper we study how the phase diagram is modified by finite size and Coulomb effects.   We show that the thermodynamic anomalies which are associated to the finite system counterpart of first order phase transitions, are correctly reproduced by this effective model. However, approximations in the calculation of the grandcanonical partition sum prevent obtaining the exact mapping between statistical ensembles which should be associated to finite systems. The ensemble inequivalence associated to the transition persists in the presence of Coulomb, but the phase diagram is deeply modified with respect to the simple liquid-gas phase transition characteristic of the neutral system.
For viable applications, spintronic devices based e.g. on domain wall motion need to be highly reliable with stable magnetization states and highly reproducible switching pathways transforming one state to another. The existence of multiple stable states and switching pathways in a system is a definitive barrier for device operation, yet rare and stochastic events are difficult to detect and understand. We demonstrate an approach to quantify competing magnetic states and stochastic switching pathways based on time-resolved scanning electron microscopy with polarization analysis, applied to the technologically relevant control of vortex domain wall chirality via field and curvature in curved wires. While being a pump-probe technique, our analysis scheme nonetheless allows for the disentanglement of different occurring dynamic pathways and we can even identify the rare events leading to changes from one magnetization switching pathway to another pathway via temperature- and geometry-dependent measurements. The experimental imaging is supported by micromagnetic simulations to reveal the mechanisms responsible for the change of the pathway. Together the results allow us to explain the origin and details of the domain wall chirality control and to quantify the frequency and the associated energy barriers of thermally activated changes of the states and switching pathways.
For a sequence $d$ of non-negative integers, let ${\cal G}(d)$ and ${\cal F}(d)$ be the sets of all graphs and forests with degree sequence $d$, respectively. Let $\gamma_{\min}(d)=\min\{ \gamma(G):G\in {\cal G}(d)\}$, $\alpha_{\max}(d)=\max\{ \alpha(G):G\in {\cal G}(d)\}$, $\gamma_{\min}^{\cal F}(d)=\min\{ \gamma(F):F\in {\cal F}(d)\}$, and $\alpha_{\max}^{\cal F}(d)=\max\{ \alpha(F):F\in {\cal F}(d)\}$ where $\gamma(G)$ is the domination number and $\alpha(G)$ is the independence number of a graph $G$. Adapting results of Havel and Hakimi, Rao showed in 1979 that $\alpha_{\max}(d)$ can be determined in polynomial time.   We establish the existence of realizations $G\in {\cal G}(d)$ with $\gamma_{\min}(d)=\gamma(G)$, and $F_{\gamma},F_{\alpha}\in {\cal F}(d)$ with $\gamma_{\min}^{\cal F}(d)=\gamma(F_{\gamma})$ and $\alpha_{\max}^{\cal F}(d)=\alpha(F_{\alpha})$ that have strong structural properties. This leads to an efficient algorithm to determine $\gamma_{\min}(d)$ for every given degree sequence $d$ with bounded entries as well as closed formulas for $\gamma_{\min}^{\cal F}(d)$ and $\alpha_{\max}^{\cal F}(d)$.
We study the Q^2 evolution of the nucleon's chiral-odd twist-3 distribution h_L(x,Q^2) starting from the MIT bag model calculation. A simple GLAP equation for h_L(x,Q^2) obtained at large N_c is used for the Q^2 evolution. The correction due to the finite value of N_c is O(1/N_c^2)\sim 10% level. It turns out that the twist-3 contribution to h_L(x,Q^2) is significantly reduced at Q^2=10 GeV^2 in contrast to the g_2(x,Q^2) case. This is due to the fact that the corresponding anomalous dimension for h_L is larger than that for g_2 at small n (spin).
The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system aparts from the typical Arrhenius relaxation to a Vogel-Fulcher-Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel-Fulcher-Tamann dynamical slowing down and the freezing mechanism.
The double-tetrahedral chain in a longitudinal magnetic field, whose nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular plaquettes with the dynamics described by the Hubbard model, is rigorously investigated. It is demonstrated that the uniform change of electron concentration controlled by the chemical potential in a combination with the competition between model parameters and the external magnetic field leads to the formation of one chiral and seven non-chiral phases at the absolute zero temperature. Rational plateaux at one-third and one-half of the saturation magnetization can also be identified in the low-temperature magnetization curves. On the other hand, the gradual electron doping results in eleven different ground-state regions which distinguish from each other by the evolution of the electron distribution during this process. Several doping-dependent magnetization plateaux are observed in the magnetization process as a result of the continuous change of electron content in the model.
We used classical and accelerated molecular dynamics simulations to characterize vacancy-mediated diffusion of cations in Gd$_2$Ti$_2$O$_7$ pyrochlore as a function of the disorder on the microsecond timescale. We find that cation vacancy diffusion is slow in materials with low levels of disorder. However, higher levels of disorder allow for fast cation diffusion, which is then also accompanied by fast antisite annihilation and ordering of the cations. The cation diffusivity is therefore not constant, but decreases as the material reorders. The results suggest that fast cation diffusion is triggered by the existence of a percolation network of antisites. This is in marked contrast with oxygen diffusion, which showed a smooth increase of the ionic diffusivity with increasing disorder in the same compound. The increase of the cation diffusivity with disorder is also contrary to observations from other complex oxides and disordered media models, suggesting a fundamentally different relation between disorder and mass transport. These results highlight the dynamic interplay between fast cation diffusion and the recovery of disorder and have important implications for understanding radiation damage evolution, sintering and aging, as well as diffusion in disorder oxides more generally.
We present 8-13 micron imaging and spectroscopy of 9 type 1 and 10 type 2 AGN obtained with the VLT/VISIR instrument at spatial resolution <100 pc. The emission from the host galaxy sources is resolved out in most cases. The silicate absorption features are moderately deep and emission features are shallow. We compare the mid-IR luminosities to AGN luminosity tracers and found that the mid-IR radiation is emitted quite isotropically. In two cases, IC5063 and MCG-3-34-64, we find evidence for extended dust emission in the narrow-line region. We confirm the correlation between observed silicate feature strength and Hydrogen column density recently found in Spitzer data. In a further step, our 3D clumpy torus model has been used to interpret the data. We show that the strength of the silicate feature and the mid-IR spectral index can be used to get reasonable constraints on the dust distribution in the torus. The mid-IR spectral index, alpha, is almost exclusively determined by the radial dust distribution power-law index, a, and the silicate feature depth is mostly depending on the average number of clouds, N0, along an equatorial line-of-sight and the torus inclination. A comparison of model predictions to our type 1 and type 2 AGN reveals typical average parameters a=-1.0+/-0.5 and N0=5-8, which means that the radial dust distribution is rather shallow. As a proof-of-concept of this method, we compared the model parameters derived from alpha and the silicate feature to more detailed studies of IR SEDs and interferometry and found that the constraints on a and N0 are consistent. Finally, we might have found evidence that the radial structure of the torus changes from low to high AGN luminosities towards steeper dust distributions, and we discuss implications for the IR size-luminosity relation. (abridged)
A graph $G$ is defined encapsulating the number theoretic notion of the Fundamental Theorem of Arithmetic. We then provide a graph theoretic approach to the fundamental results on the coprimality of two natural numbers, through the use of an adjacency operator $\hat{\mathbf{A}}(G)$. Lastly, these results are used to give an alternate proof to the known result that there are infinitely many primes in the natural numbers $\mathbb{N}$.
We develop a temperature dependent empirical pseudopotential theory to study the electronic and optical properties of self-assembled quantum dots (QDs) at finite temperature. The theory takes the effects of both lattice expansion and lattice vibration into account. We apply the theory to the InAs/GaAs QDs. For the unstrained InAs/GaAs heterostructure, the conduction band offset increases whereas the valence band offset decreases with increasing of the temperature, and there is a type-I to type-II transition at approximately 135 K. Yet, for InAs/GaAs QDs, the holes are still localized in the QDs even at room temperature, because the large lattice mismatch between InAs and GaAs greatly enhances the valence band offset. The single particle energy levels in the QDs show strong temperature dependence due to the change of confinement potentials. Because of the changes of the band offsets, the electron wave functions confined in QDs increase by about 1 - 5%, whereas the hole wave functions decrease by about 30 - 40% when the temperature increases from 0 to 300 K. The calculated recombination energies of exciton, biexciton and charged excitons show red shifts with increasing of the temperature, which are in excellent agreement with available experimental data.