ShantanuT01/DACTYL-Pretraining huggingface dataset:
The monolayer adsorption process of interacting binary mixtures of species $A$ and $B$ on square lattices is studied through grand canonical Monte Carlo simulation in the framework of the lattice-gas model. Four different energies have been considered in the adsorption process: 1) $\epsilon_0$, interaction energy between a particle (type $A$ or $B$) and a lattice site; 2) $w_{AA}$, interaction energy between two nearest-neighbor $A$ particles; 3) $w_{BB}$, interaction energy between two nearest-neighbor $B$ particles; 4) $w_{AB}=w_{BA}$, interaction energy between two nearest-neighbors being one of type $A$ and the other of type $B$. The adsorption process has been monitored through total and partial isotherms and differential heats of adsorption corresponding to both species of the mixture. Our main interest is in the repulsive lateral interactions, where a variety of structural orderings arise in the adlayer, depending on the interaction parameters ($w_{AA}$, $w_{BB}$ and $w_{AB}$). At the end of this work, we determine the phase diagram characterizing the phase transitions occurring in the system. A nontrivial interdependence between the partial surface coverage of both species is observed.
A general calculation for the distribution of non-uniform demagnetization fields in paramagnetic bulk solids is described and the fields for various sample geometries are calculated. Cones, ellipsoids, paraboloids and hyperboloids with similar sample aspect ratios are considered. Significant differences in their demagnetization fields are observed. The calculation shows that the demagnetization field magnitudes decrease along the axis of symmetry (along $z$) where an externally applied magnetic field is aligned, and increase in the vicinity of the lateral surfaces with the largest field values found in the cone and the narrowest field distributions found in the hyperboloid. Application is made to the theoretical modeling of the $^{1}$H-NMR spectra of a single crystal of field-induced superconductor $\lambda$-(BETS)$_{2}$FeCl$_{4}$ with a rectangular sample geometry, providing a good fit to the measured NMR spectra. This calculation is also applicable to diamagnetic or ferromagnetic materials in general.
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields the multi-coordinate Schr\"odinger equation, with its usual boundary conditions, as an essential statistical equation for the system. We derive the general "canonical quantization" rule, that the Hamiltonian operator must be the classical Hamiltonian in the $N$-dimensional metric configuration space defined by the classical kinetic energy of the system, with the classical conjugate momentum $N$-vector replaced by $-i\hbar$ times the vector gradient operator in that space. We obtain these results by using conservation of probability, general tensor calculus, the Madelung transform, the Ehrenfest theorem and/or the Hamilton-Jacobi equation, and comparison with results for the charged harmonic oscillator in stochastic electrodynamics. We also provide two illustrative examples and a discussion of how coordinate trajectories could be compatible with wave properties such as interference, diffraction, and tunneling.
Let $U$ be a smooth scheme over an algebraically closed field $\mathbb K$ of characteristic zero and $f:U\to{\mathbb A}^1$ a regular function, and write $X=$Crit$(f)$, as a closed subscheme of $U$. The motivic vanishing cycle $MF_{U,f}^\phi$ is an element of the $\hat\mu$-equivariant motivic Grothendieck ring ${\mathcal M}^{\hat\mu}_X$ defined by Denef and Loeser math.AG/0006050 and Looijenga math.AG/0006220, and used in Kontsevich and Soibelman's theory of motivic Donaldson-Thomas invariants, arXiv:0811.2435.   We prove three main results:   (a) $MF_{U,f}^\phi$ depends only on the third-order thickenings $U^{(3)},f^{(3)}$ of $U,f$.   (b) If $V$ is another smooth scheme, $g:V\to{\mathbb A}^1$ is regular, $Y=$Crit$(g)$, and $\Phi:U\to V$ is an embedding with $f=g\circ\Phi$ and $\Phi\vert_X:X\to Y$ an isomorphism, then $\Phi\vert_X^*(MF_{V,g}^\phi)$ equals $MF_{U,f}^\phi$ "twisted" by a motive associated to a principal ${\mathbb Z}_2$-bundle defined using $\Phi$, where now we work in a quotient ring $\bar{\mathcal M}^{\hat\mu}_X$ of ${\mathcal M}^{\hat\mu}_X$.   (c) If $(X,s)$ is an "oriented algebraic d-critical locus" in the sense of Joyce arXiv:1304.4508, there is a natural motive $MF_{X,s} \in\bar{\mathcal M}^{\hat\mu}_X$, such that if $(X,s)$ is locally modelled on Crit$(f:U\to{\mathbb A}^1)$, then $MF_{X,s}$ is locally modelled on $MF_{U,f}^\phi$.   Using results from arXiv:1305.6302, these imply the existence of natural motives on moduli schemes of coherent sheaves on a Calabi-Yau 3-fold equipped with "orientation data", as required in Kontsevich and Soibelman's motivic Donaldson-Thomas theory arXiv:0811.2435, and on intersections of oriented Lagrangians in an algebraic symplectic manifold.   This paper is an analogue for motives of results on perverse sheaves of vanishing cycles proved in arXiv:1211.3259. We extend this paper to Artin stacks in arXiv:1312.0090.
In light of a new experiment which claims an identification of tetraneutron [3], we discuss the results of experimental search of trineutron and tetraneutron in different nuclear reactions. A summary of theoretical studies for trineutron and tetraneutron within variety of approaches such as variational methods, the method of Faddeev and Faddeev-Yakubovsky equations, and the method of hyperspherical harmonics are presented.
The two objects 1SWASP J150822.80-054236.9 and 1SWASP J160156.04+202821.6 were initially detected from their SuperWASP archived light curves as candidate eclipsing binaries with periods close to the short-period cut-off of the orbital period distribution of main sequence binaries, at ~0.2 d. Here, using INT spectroscopic data, we confirm them as double-lined spectroscopic and eclipsing binaries, in contact configuration. Following modelling of their visual light curves and radial velocity curves, we determine their component and system parameters to precisions between ~2 and 11%. The former system contains 1.07 and 0.55 M_sun components, with radii of 0.90 and 0.68 R_sun respectively; its primary exhibits pulsations with period 1/6 the orbital period of the system. The latter contains 0.86 and 0.57 M_sun components, with radii of 0.75 and 0.63R_sun respectively.
Hexagonal boron nitride is a wide bandgap semiconductor with a very high thermal and chemical stability often used in devices operating under extreme conditions. The growth of high-purity crystals has recently revealed the potential of this material for deep ultraviolet emission, with an intense emission around 215 nm. In the last few years, hexagonal boron nitride has been raising even more attention with the emergence of two-dimensional atomic crystals and Van der Waals heterostructures, initiated with the discovery of graphene. Despite this growing interest and a seemingly simple structure, the basic questions of the bandgap nature and value are still controversial. Here, we resolve this long-debated issue by bringing the evidence for an indirect bandgap at 5.955 eV by means of optical spectroscopy. We demonstrate the existence of phonon-assisted optical transitions, and we measure an exciton binding energy of about 130 meV by two-photon spectroscopy.
We consider a branching-selection particle system on $\Z$ with $N \geq 1$ particles. During a branching step, each particle is replaced by two new particles, whose positions are shifted from that of the original particle by independently performing two random walk steps according to the distribution $p \delta_{1} + (1-p) \delta_{0}$, from the location of the original particle. During the selection step that follows, only the N rightmost particles are kept among the 2N particles obtained at the branching step, to form a new population of $N$ particles. After a large number of iterated branching-selection steps, the displacement of the whole population of $N$ particles is ballistic, with deterministic asymptotic speed $v_{N}(p)$. As $N$ goes to infinity, $v_{N}(p)$ converges to a finite limit $v_{\infty}(p)$. The main result is that, for every $0<p<1/2$, as $N$ goes to infinity, the order of magnitude of the difference $v_{\infty}(p)- v_{N}(p)$ is $\log(N)^{-2}$. This is called Brunet-Derrida behavior in reference to the 1997 paper by E. Brunet and B. Derrida "Shift in the velocity of a front due to a cutoff" (see the reference within the paper), where such a behavior is established for a similar branching-selection particle system, using both numerical simulations and heuristic arguments.
We show that in an SU(3)_c\times [SU(2)_L\times U(1)_Y]\times [SU(2)'_R\times U(1)'_Y] framework, the parity symmetry motivated by solving the strong CP problem without resorting to an axion can predict a dark matter particle with a mass around 302 GeV. This dark matter candidate can be directly detected in the presence of a U(1)_Y\times U(1)'_Y kinetic mixing. Furthermore, our model can accommodate a natural way to simultaneously realize an inverse-linear seesaw for neutrino masses and a resonant leptogenesis for baryon asymmetry.
The temperature-dependent evolution pattern of 5f electrons helps to elucidate the long-standing itinerant-localized dual nature in plutonium-based compounds. In this work, we investigate the correlated electronic states of PuIn3 dependence on temperature by using a combination of the density functional theory and the dynamical mean-field theory. Not only the experimental photoemission spectroscopy is correctly reproduced, but also a possible hidden 5f itinerant-localized crossover is identified. Moreover, it is found that the quasiparticle multiplets from the many-body transitions gradually enhance with decreasing temperature, accompanied by the hybridizations with 5f electrons and conduction bands. The temperature-induced variation of Fermi surface topology suggests a possible electronic Lifshitz transition and the onset of magnetic order at low temperature. Finally, the ubiquitous existence orbital selective 5f electron correlation is also discovered in PuIn3. These illuminating results shall enrich the understanding on Pu-based compounds and serve as critical predictions for ongoing experimental research.
We survey recent developments in the theory of impartial combinatorial games in misere play, focusing on how the Sprague-Grundy theory of normal-play impartial games generalizes to misere play via the indistinguishability quotient construction.
Mechanisms involved in the star formation process and in particular the duration of the different phases of the cloud contraction are not yet fully understood. Photometric data alone suggest that objects coexist in the young cluster NGC6530 with ages from ~1 Myr up to 10 Myrs. We want to derive accurate stellar parameters and, in particular, stellar ages to be able to constrain a possible age spread in the star-forming region NGC6530. We used low-resolution spectra taken with VIMOS@VLT and literature spectra of standard stars to derive spectral types of a subsample of 94 candidate members of this cluster. We assign spectral types to 86 of the 88 confirmed cluster members and derive individual reddenings. Our data are better fitted by the anomalous reddening law with R$_{\rm V}$=5. We confirm the presence of strong differential reddening in this region. We derive fundamental stellar parameters, such as effective temperatures, photospheric colors, luminosities, masses, and ages for 78 members, while for the remaining 8 YSOs we cannot determine the interstellar absorption, since they are likely accretors, and their V-I colors are bluer than their intrinsic colors. The cluster members studied in this work have masses between 0.4 and 4 M$_\odot$ and ages between 1-2 Myrs and 6-7 Myrs. We find that the SE region is the most recent site of star formation, while the older YSOs are loosely clustered in the N and W regions. The presence of two distint generations of YSOs with different spatial distribution allows us to conclude that in this region there is an age spread of ~6-7 Myrs. This is consistent with the scenario of sequential star formation suggested in literature.
In this paper, we define and study a variant of multiple zeta values of level 2 (which is called multiple mixed values or multiple $M$-values, MMVs for short), which forms a subspace of the space of alternating multiple zeta values. This variant includes both Hoffman's multiple $t$-values and Kaneko-Tsumura's multiple $T$-values as special cases. We set up the algebra framework for the double shuffle relations (DBSFs) of the MMVs, and exhibits nice properties such as duality, integral shuffle relation, series stuffle relation, etc., similar to ordinary multiple zeta values. Moreover, we study several $T$-variants of Kaneko-Yamamoto type multiple zeta values by establishing some explicit relations between these $T$-variants and Kaneko-Tsumura $\psi$-values. Furthermore, we prove that all Kaneko-Tsumura $\psi$-values can be expressed in terms of Kaneko-Tsumura multiple $T$-values by using multiple associated integrals, and find some duality formulas for Kaneko-Tsumura $\psi$-values. We also discuss the explicit evaluations for a kind of MMVs of depth two and three by using the method of contour integral and residue theorem. Finally, we investigate the dimensions of a few interesting subspaces of MMVs for small weights.
The mechanism causing breaks in the radial surface brightness distribution of spiral galaxies is not yet well known. Despite theoretical efforts, there is not a unique explanation for these features and the observational results are not conclusive. In an attempt to address this problem, we have selected a sample of 34 highly inclined spiral galaxies present both in the Sloan Digital Sky Survey and in the Spitzer Survey of Stellar Structure in Galaxies. We have measured the surface brightness profiles in the five Sloan optical bands and in the 3.6$\mu m$ Spitzer band. We have also calculated the color and stellar surface mass density profiles using the available photometric information, finding two differentiated features: an innermost break radius at distances of $\sim 8 \pm 1$ kpc [$0.77 \pm 0.06$ $R_{25}$] and a second characteristic radius, or truncation radius, close to the outermost optical extent ($\sim 14 \pm 2$ kpc [$1.09 \pm 0.05$ $R_{25}$]) of the galaxy. We propose in this work that the breaks might be a phenomena related to a threshold in the star formation, while truncations are more likely a real drop in the stellar mass density of the disk associated with the maximum angular momentum of the stars.
Density functional calculations are performed to study the magnetic order of the severely distorted square planar cupric oxide (CuO) and local spin disorder in it in the presence of the transition metal impurities M (= Cr, Mn, Fe, Co and Ni). The distortion in the crystal structure, arisen to reduce the band energy by minimizing the covalent interaction, creates two crisscrossing zigzag spin-1/2 chains. From the spin dimer analysis we find that while the spin chain along [10$\bar 1$] has strong Heisenberg type antiferromagnetic coupling (J ~ 127 meV), along [101] it exhibits weak, but robust, ferromagnetic coupling (J ~ 9 meV) mediated by reminiscent p-d covalent interactions. The impurity effect on the magnetic ordering is independent of M and purely orbital driven. If the given spin-state of M is such that the d$_{x^2-y^2}$ orbital is spin-polarized, then the original long-range ordering is maintained. However, if d$_{x^2-y^2}$ orbital is unoccupied, the absence of corresponding covalent interaction breaks the weak ferromagnetic coupling and a spin-flip takes place at the impurity site leading to breakdown of the long range magnetic ordering.
We study a Luttinger Liquid in a finite one-dimensional wire with box-like boundary conditions by considering the local distribution of the single particle spectral weight. This corresponds to the experimental probability of extracting a single electron at a given place and energy, which can be interpreted as the square of an electron wave-function. For the non-interacting case, this is given by a standing wave at the Fermi wave-vector. In the presence of interactions, however, the wave-functions obtain additional structure with a sharp depletion near the edges and modulations throughout the wire. In the spinful case, these modulations correspond to the separate spin- and charge-like excitations in the system.
This paper summarizes some highlights from the Pierre Auger Observatory that were presented at the ICRC 2011 in Beijing. The cumulative exposure has grown by more than 60% since the previous ICRC to above 21000 km^2 sr yr. Besides giving important updates on the energy spectrum, mass composition, arrival directions, and photon- and neutrino upper limits, we present first measurements of the energy spectrum down to 3 x 10^{17} eV, first distributions of the shower maximum, X_max, together with new surface detector related observables sensitive to X_max, and we present first measurements of the p-air cross section at ~ 10^{18} eV. Serendipity observations such as of atmospheric phenomena showing time evolutions of elves extend the breadth of the astrophysics research program.
In this paper, we prove that for any totally real field $F$, weight $k$, and nebentypus character $\chi$, the proportion of Hilbert cusp forms over $F$ of weight $k$ and character $\chi$ with bounded field of rationality approaches zero as the level grows large. This answers, in the affirmative, a question of Serre. The proof has three main inputs: first, a lower bound on fields of rationality for admissible $GL_2$ representations; second, an explicit computation of the (fixed-central-character) Plancherel measure for $GL_2$; and third, a Plancherel equidsitribution theorem for cusp forms with fixed central character. The equidistribution theorem is the key intermediate result and builds on earlier work of Shin and Shin-Templier and mirrors work of Finis-Lapid-Mueller by introducing an explicit bound for certain families of orbital integrals.
Recent progress in the three-dimensional modeling of supernovae (SN) has shown the importance of asymmetries for the explosion. This calls for a reconsideration of the modeling of the subsequent phase, the supernova remnant (SNR), which has commonly relied on simplified ejecta models. In this paper we bridge SN and SNR studies by using the output of a SN simulation as the input of a SNR simulation carried on until 500~yr. We consider the case of a thermonuclear explosion of a carbon-oxygen white dwarf star as a model for a Type Ia SN; specifically we use the N100 delayed detonation model of Seitenzahl et al 2013. In order to analyze the morphology of the SNR, we locate the three discontinuities that delineate the shell of shocked matter: the forward shock, the contact discontinuity, and the reverse shock, and we decompose their radial variations as a function of angular scale and time. Assuming a uniform ambient medium, we find that the impact of the SN on the SNR may still be visible after hundreds of years. Previous 3D simulations aiming at reproducing Tycho's SNR, that started out from spherically symmetric initial conditions, failed to reproduce structures at the largest angular scales observed in X-rays. Our new simulations strongly suggest that the missing ingredient was the initial asymmetries from the SN itself. With this work we establish a way of assessing the viability of SN models based on the resulting morphology of the SNR.
Background: The trend towards large-scale studies including population imaging poses new challenges in terms of quality control (QC). This is a particular issue when automatic processing tools, e.g. image segmentation methods, are employed to derive quantitative measures or biomarkers for later analyses. Manual inspection and visual QC of each segmentation isn't feasible at large scale. However, it's important to be able to automatically detect when a segmentation method fails so as to avoid inclusion of wrong measurements into subsequent analyses which could lead to incorrect conclusions. Methods: To overcome this challenge, we explore an approach for predicting segmentation quality based on Reverse Classification Accuracy, which enables us to discriminate between successful and failed segmentations on a per-cases basis. We validate this approach on a new, large-scale manually-annotated set of 4,800 cardiac magnetic resonance scans. We then apply our method to a large cohort of 7,250 cardiac MRI on which we have performed manual QC. Results: We report results used for predicting segmentation quality metrics including Dice Similarity Coefficient (DSC) and surface-distance measures. As initial validation, we present data for 400 scans demonstrating 99% accuracy for classifying low and high quality segmentations using predicted DSC scores. As further validation we show high correlation between real and predicted scores and 95% classification accuracy on 4,800 scans for which manual segmentations were available. We mimic real-world application of the method on 7,250 cardiac MRI where we show good agreement between predicted quality metrics and manual visual QC scores. Conclusions: We show that RCA has the potential for accurate and fully automatic segmentation QC on a per-case basis in the context of large-scale population imaging as in the UK Biobank Imaging Study.
We study the Hamiltonian motion of an ensemble of unconfined classical particles driven by an external field F through a translationally-invariant, thermal array of monochromatic Einstein oscillators. The system does not sustain a stationary state, because the oscillators cannot effectively absorb the energy of high speed particles. We nonetheless show that the system has at all positive temperatures a well-defined low-field mobility over macroscopic time scales of order exp(-c/F). The mobility is independent of F at low fields, and related to the zero-field diffusion constant D through the Einstein relation. The system therefore exhibits normal transport even though the bath obviously has a discrete frequency spectrum (it is simply monochromatic) and is therefore highly non-Ohmic. Such features are usually associated with anomalous transport properties.
We study the superfluid to Mott-insulator (SF-MI) transition of hardcore bosons in commensurate superlattices in two and three dimensions. We focus on the special case where the superlattice has period two and the system is at half filling. We obtain exact numerical results by using the stochastic series expansion (SSE) algorithm, and compute various properties of the system, such as the ground-state energy, the fraction of bosons in the zero-momentum mode, the superfluid density, and the compressibility. With finite-size scaling, we find the critical points of the phase transition. We also explore the extent to which several approximate solutions such as mean-field theory, with and without spin-wave corrections, can help one gain analytical insight into the behavior of the system in the vicinity of the phase transition.