ShantanuT01/DACTYL-Pretraining huggingface dataset:
We derive sharp upper and lower bounds on the number of intersection points and closed regions that can occur in sets of line segments with certain structure, in terms of the number of segments. We consider sets of segments whose underlying planar graphs are Halin graphs, cactus graphs, maximal planar graphs, and triangle-free planar graphs, as well as randomly produced segment sets. We also apply these results to a variant of the Erd\H{o}s-Faber-Lov\'asz (EFL) Conjecture stating that the intersection points of $m$ segments can be colored with $m$ colors so that no segment contains points with the same color. We investigate an optimization problem related to the EFL Conjecture for line segments, determine its complexity, and provide some computational approaches.
We study the intersection of two copies of $\mathrm{Gr}(2,5)$ embedded in $\mathbf{P}^9$, and the intersection of the two projectively dual Grassmannians in the dual projective space. These intersections are deformation equivalent, derived equivalent Calabi-Yau threefolds. We prove that generically they are not birational. As a consequence, we obtain a counterexample to the birational Torelli problem for Calabi-Yau threefolds. We also show that these threefolds give a new pair of varieties whose classes in the Grothendieck ring of varieties are not equal, but whose difference is annihilated by a power of the class of the affine line. Our proof of non-birationality involves a detailed study of the moduli stack of Calabi-Yau threefolds of the above type, which may be of independent interest.
We study a graph based version of the Ohta-Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a variational model for pattern formation.   Graph based problems inspired by partial differential equations (PDEs) and varational methods have been the subject of many recent papers in the mathematical literature, because of their applications in areas such as image processing and data classification. This paper extends the area of PDE inspired graph based problems to pattern forming models, while continuing in the tradition of recent papers in the field.   We introduce a mass conserving Merriman-Bence-Osher (MBO) scheme for minimizing the graph Ohta-Kawasaki functional with a mass constraint. We present three main results: (1) the Lyapunov functionals associated with this MBO scheme $\Gamma$-converge to the Ohta-Kawasaki functional (which includes the standard graph based MBO scheme and total variation as a special case); (2) there is a class of graphs on which the Ohta-Kawasaki MBO scheme corresponds to a standard MBO scheme on a transformed graph and for which generalized comparison principles hold; (3) this MBO scheme allows for the numerical computation of (approximate) minimizers of the graph Ohta-Kawasaki functional with a mass constraint.
In this paper, we continue to study properties of rational approximations to Euler's constant and values of the Gamma function defined by linear recurrences, which were found recently by A. I. Aptekarev and T. Rivoal. Using multiple Jacobi-Laguerre orthogonal polynomials we present rational approximations to the quotient of values of the Gamma function at rational points. As a limit case of our result, we obtain new explicit formulas for numerators and denominators of the Aptekarev approximants to Euler's constant.
We find a characterization for Fano 4-folds $X$ with Lefschetz defect $\delta_{X}=3$: besides the product of two del Pezzo surfaces, they correspond to varieties admitting a conic bundle structure $f\colon X\to Y$ with $\rho_{X}-\rho_{Y}=3$. Moreover, we observe that all of these varieties are rational. We give the list of all possible targets of such contractions. Combining our results with the classification of toric Fano $4$-folds due to Batyrev and Sato we provide explicit examples of Fano conic bundles from toric $4$-folds with $\delta_{X}=3$.
The electronic structure of the transparent semiconductor In2O3 has been studied by angle resolved photoemission spectroscopy upon deposition of metallic indium and also tin on the surface of the semiconductor. By deposition of metallic indium on In2O3 (111) single crystals, we detected the formation of a free-electron like band of effective mass (0.38+-0.05) m0. At low coverages, metallic In shifts the Fermi level of In2O3 to higher energies and a new electronic state forms at the metal/semiconductor interface. This state of two-dimensional character (2D-electron gas) is completely responsible for the electrical conduction in In2O3 (111) at the surface region and has a band dispersion, which does not correspond to the previously found surface accumulation layers in this material. Despite the similarity of the electronic properties of In and Sn, a larger downward banding was observed by Sn coverage, which was not accompanied by the appearance of the surface state.
We report dissipative magnon-photon coupling caused by cavity Lenz effect, where the magnons in a magnet induce a rf current in the cavity, leading to a cavity back action that impedes the magnetization dynamics. This effect is revealed in our experiment as level attraction with a coalescence of hybridized magnon-photon modes, which is distinctly different from level repulsion with mode anticrossing caused by coherent magnon-photon coupling. We develop a method to control the in- terpolation of coherent and dissipative magnon-photon coupling, and observe a matching condition where the two effects cancel. Our work sheds light on the so-far hidden side of magnon-photon coupling, opening a new avenue for controlling and utilizing light-matter interactions.
We shall show that $9$ is the only odd infinitary superperfect numbers.
We investigate the evolution of compact galaxy number density over the redshift range $0.2<z<0.8$. Our sample consists of galaxies with secure spectroscopic redshifts observed in the COSMOS field. With the large uncertainties, the compact galaxy number density trend with redshift is consistent with a constant value over the interval $0.2<z<0.8$. Our number density estimates are similar to the estimates at $z>1$ for equivalently selected compact samples. Small variations in the abundance of the COSMOS compact sources as a function of redshift correspond to known structures in the field. The constancy of the compact galaxy number density is robust and insensitive to the compactness threshold or the stellar mass range (for $M_\ast>10^{10}\, M_\odot$). To maintain constant number density any size growth of high-redshift compact systems with decreasing redshift must be balanced by formation of quiescent compact systems at $z<1$.
We give an overview of recent work on charge degrees of freedom of strongly correlated electrons on geometrically frustrated lattices. Special attention is paid to the checkerboard lattice, i.e., the two-dimensional version of a pyrochlore lattice and to the kagome lattice. For the checkerboard lattice it is shown that at half filling when spin degrees of freedom are neglected and quarter filling when they are included excitations with fractional charges $\pm$e/2 may exist. The same holds true for the three-dimensional pyrochlore lattice. In the former case the fractional charges are confined. The origin of the weak constant confining force is discussed and some similarities to quarks and to string theory are pointed out. For the checkerboard lattice a formulation in terms of a compact U(1) gauge theory is described. Furthermore a new kinetic mechanism for ferromagnetism at special fillings of a kagome lattice is discussed.
An approach for calculation of transition form factors of hydrogen-like elementary atoms (EA) is proposed. A general formula for bound-continuous transition form factors of EA is derived. It is shown that these form factors can be represented in the form of finite sum of terms with simple analytical structure and may be numerically evaluated with arbitrary degree of accuracy. As an application of the presented form factors, the calculation of the spectra of products from EA ionization is considered.
We aim to study the optical and near-infrared linear polarimetric properties of a sample of young M7-L7 dwarfs ($\approx$1-500 Myr) with spectroscopic signatures of low- and intermediate-gravity atmospheres. We collected optical ($RIZ$) and near-infrared ($YJHK_{\rm s}$) linear polarimetry images on various time scales from $\sim$0.2 h to months. Linear polarization degrees in the interval 0-1.5\% ($I$- and $J$-bands) were measured with accuracies ranging from $\pm$0.1 $\%$ to $\pm$0.9 $\%$ depending on the observing filter and the target brightness. We found that the young field dwarfs in our sample show similar polarimetric degrees at both $I$- and $J$-bands, and that there is no obvious trend with the spectral type. The two Taurus sources in our sample show intense levels of $J$-band linear polarization probably due to surrounding disks. By compiling data from the literature for high-gravity M7-L7 dwarfs with likely ages $\ge$500 Myr, we did not observe any apparent difference in the linear polarimetry intensity between the young and old samples that could be ascribed to differing atmospheric gravities. Polarimetric variability with peak to peak amplitudes up to 1.5 $\%$ is detected on scales of about a rotation in two out of four targets that were monitored over several hours. Long-term polarimetric variability is also detected in nearly all dwarfs of the sample with data spanning months to years.
I advocate the virtues of a very economical version of the minimal supersymmetric standard model which avoids cosmological problems often encountered in dynamical SUSY-breaking and solves the SUSY-CP problem. Imposing $m_Z=91$ GeV and $m_t \sim 175$ GeV implies that scalar masses are generally $100-200$ GeV. The gluino and photino are massless at tree level. At 1-loop, the gluino mass is predicted to be in the range $m_{\gluino}: 100 - 600$ MeV and the photino mass can be estimated to be $m_{\photino}: 100 - 1400$ MeV. New hadrons with mass $\sim 1 \frac{1}{2}$ GeV are predicted and described. The ``extra'' flavor singlet pseudoscalar observed in two experiments in the $\iota(1440)$ region, if confirmed, is naturally interpreted as the state which gets its mass via the QCD anomaly. Its superpartner, a gluon-gluino bound state, generally has a lifetime longer than $5~10^{-11}$ sec and would not have shown up in existing searches. Search strategies and other consequences of the scenario are discussed.
In this paper, we describe the spaces of stability conditions for the triangulated categories associated to three dimensional Calabi-Yau fibrations. We deal with two cases, the flat elliptic fibrations and smooth K3 (Abelian) fibrations. In the first case, we will see there exist chamber structures similar to those of the movable cone used in birational geometry. In the second case, we will compare the space with the space of stability conditions for the closed fiber of the fibration.
In the framework of the theory of open systems, we give a description of quantum entanglement and quantum discord for two non-interacting modes embedded in a thermal environment. We describe the evolution of entanglement in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable squeezed thermal state remains separable for all times. In the case of an entangled initial squeezed thermal state, entanglement suppression (entanglement sudden death) takes place, for non-zero temperatures of the environment. The Gaussian quantum discord, which is a measure of all quantum correlations in the state, including entanglement, decays asymptotically in time.
We study the formation and evolution of jets in the solar atmosphere using numerical simulations of partially ionized plasma. The two-fluid magnetohydrodynamic equations with ion+electron and neutral hydrogen components are used in two-dimensional (2D) Cartesian geometry. Numerical simulations show that a localized nonlinear Gaussian pulse of ion and neutral pressures initially launched from the magnetic null point of a potential arcade located below the transition region quickly develops into a shock due to the decrease of density with height. The shock propagates upwards into the solar corona and lifts the cold and dense chromospheric plasma behind in the form of a collimated jet with an inverted-Y shape. The inverted-Y shape of jets is connected with the topology of a magnetic null point. The pulse also excites a nonlinear wake in the chromosphere, which leads to quasi-periodic secondary shocks. The secondary shocks lift the chromospheric plasma upwards and create quasi-periodic jets in the lower corona. Ion and neutral fluids show generally similar behavior, but their relative velocity is higher near the upper part of jets, which leads to enhanced temperature or heating due to ion-neutral collisions. Simulations of jets with inverted-Y shape and their heating may explain the properties of some jets observed in the solar atmosphere.
Operating experience from fusion research shows how Spitzer resistivity may render ohmic heating in the chromosphere self limiting and thus serve to define the lower margin of the transition region. Its upper margin is at about 6000 K, where radiative cooling of He:H plasma decelerates sharply. The third and last stage in the proposed scheme is expansion into the tenuous plasma of space, which leads to the acceleration of ions to high energies, long recorded by spacecraft instruments. There is thus dynamic continuity all the way from the solar interior, the energy source for spinning columns in the Rayleigh Benard setting of the convection zone, to the coronal exhalation of the solar wind, a finding which should benefit the analysis of space weather, witness the association between helium in the solar wind and the incidence of coronal mass ejections.
Octonion creation and annihilation operators are used to construct the Standard Model plus Gravity. The resulting phenomenological model is the D4-D5-E6 model described in hep-ph/9501252 .
Fission fragments' charge and mass distribution is an important input to applications ranging from basic science to energy production or nuclear non-proliferation. In simulations of nucleosynthesis or calculations of superheavy elements, these quantities must be computed from models, as they are needed in nuclei where no experimental information is available. Until now, standard techniques to estimate these distributions were not capable of accounting for fine-structure effects, such as the odd-even staggering of the charge distributions. In this work, we combine a fully-microscopic collective model of fission dynamics with a recent extension of the particle number projection formalism to provide the highest-fidelity prediction of the primary fission fragment distributions for the neutron-induced fission of $^{235}$U and $^{239}$Pu. We show that particle number projection is an essential ingredient to reproduce odd-even staggering in the charge yields and benchmark the performance of various empirical probability laws that could simulate its effect. This new approach also enables for the first time the realistic determination of two-dimensional isotopic yields within nuclear density functional theory.
The line intensities of the fundamental rotational transitions of H13CN and HC15N were observed towards two prestellar cores, L183 and L1544, and lead to molecular isotopic ratios 140 6 14N/15N 6 250 and 140 6 14N/15N 6 360, respectively. The range of values reflect genuine spatial variations within the cores. A comprehensive analysis of the available measurements of the nitrogen isotopic ratio in prestellar cores show that molecules carrying the nitrile functional group appear to be systematically 15N-enriched com- pared to those carrying the amine functional group. A chemical origin for the differential 15N-enhance- ment between nitrile- and amine-bearing interstellar molecules is proposed. This sheds new light on several observations of Solar System objects: (i) the similar N isotopic fractionation in Jupiter's NH3 and solar wind N+; (ii) the 15N-enrichments in cometary HCN and CN (that might represent a direct inter- stellar inheritance); and (iii) 15N-enrichments observed in organics in primitive cosmomaterials. The large variations in the isotopic composition of N-bearing molecules in Solar System objects might then simply reflect the different interstellar N reservoirs from which they are originating.
The solar-activity-cycle minimum observed between Cycles 23 and 24 is generally regarded as being unusually deep and long. That minimum is being followed by one of the smallest amplitude cycles in recent history. We perform an in-depth analysis of this minimum with helioseismology. We use Global Oscillation Network Group (GONG) data to demonstrate that the frequencies of helioseismic oscillations are a sensitive probe of the Sun's magnetic field: The frequencies of the helioseismic oscillations were found to be systematically lower in the minimum following Cycle 23 than in the minimum preceding it. This difference is statistically significant and may indicate that the Sun's global magnetic field was weaker in the minimum following Cycle 23. The size of the shift in oscillation frequencies between the two minima is dependent on the frequency of the oscillation and takes the same functional form as the frequency dependence observed when the frequencies at cycle maximum are compared with the cycle-minimum frequencies. This implies that the same near-surface magnetic perturbation is responsible. Finally, we determine that the difference in the mean magnetic field between the minimum preceding Cycle 23 and that following it is approximately 1G.
Modern population synthesis models estimate that 50% of the restframe K-band light is produced by TP-AGB stars during the first Gyr of a stellar population, with a substantial fraction continuing to be produced by the TP-AGB over a Hubble time. Between 0.2 and 1.5 Gyr, intermediate mass stars evolve into TP-AGB C stars which, due to significant amounts of circumstellar dust, emit half their energy in the mid-IR. We combine these results using published mid-IR colors of Galactic TP-AGB M and C stars to construct simple models for exploring the contribution of the TP-AGB to 24micron data as a function of stellar population age. We compare these empirical models with an ensemble of galaxies in the CDFS from z=0 to z=2, and with high quality imaging in M81. Within the uncertainties, the TP-AGB appears responsible for a substantial fraction of the mid-IR luminosities of galaxies from z=0 to z=2, the maximum redshift to which we can test our hypothesis, while, at the same time, our models reproduce much of the detailed structure observed in mid-IR imaging of M81. The mid-IR is a good diagnostic of star formation over timescales of ~1.5 Gyr, but this implies that on-going star formation rates at z=1 may be overestimated by factors of ~1.5-6, depending on the nature of star formation events. Our results, if confirmed through subsequent work, have strong implications for the star formation rate density of the universe and the growth of stellar mass over time.
The Higgs-Yukawa model in curved spacetime (renormalizable in the usual sense) is considered near the critical point, employing the $1/N$--expansion and renormalization group techniques. By making use of the equivalence of this model with the standard NJL model, the effective potential in the linear curvature approach is calculated and the dynamically generated fermionic mass is found. A numerical study of chiral symmetry breaking by curvature effects is presented.
We investigate the effects induced by spin polarization in the contacts attached to a serial double quantum dot. The polarization generates effective magnetic fields and suppresses the Kondo effect in each dot. The super-exchange interaction ($J_{\mathrm{AFM}}$), tuned by the inter-dot tunnelling rate $t$, can be used to compensate the effective fields and restore the Kondo resonance when the contact polarizations are aligned. As a consequence, the direction of the spin conductance can be controlled and even reversed using electrostatic gates alone. Furthermore, we study the associated two-impurity Kondo model and show that a ferromagnetic exchange coupling ($J_{\mathrm{FM}}$) leads to an effective spin-1 exchange-anisotropic Kondo model which exhibits a quantum phase transition in the presence of partially polarized contacts.
In a previous paper [Phys. Rev. B 85,195144 (2012)], variational Monte Carlo method (based on Gutzwiller projected states) was generalized to $S=1$ systems. This method provided very good trial ground states for the gapped phases of $S=1$ bilinear-biquadratic (BLBQ) Heisenberg chain. In the present paper, we extend the approach to study the low-lying elementary excitations in $S=1$ chains. We calculate the one-magnon and two-magnon excitation spectra of the BLBQ Heisenberg chain and the results agree very well with recent data in literature. In our approach, the difference of the excitation spectrum between the Haldane phase and the dimer phase (such as the even/odd size effect) can be understood from their different topology of corresponding mean field theory. We especially study the Takhtajan-Babujian critical point. Despite the fact that the `elementary excitations' are spin-1 magnons which are different from the spin-1/2 spinons in Bethe solution, we show that the excitation spectrum, critical exponent ($\eta=0.74$) and central charge ($c=1.45$) calculated from our theory agree well with Bethe ansatz solution and conformal field theory predictions.
We consider a (1+1)-dimensional ballistic deposition process with next-nearest neighbor interaction, which belongs to the KPZ universality class, and introduce for this discrete model a variational formulation similar to that for the randomly forced continuous Burgers equation. This allows to identify the characteristic structures in the bulk of a growing aggregate ("clusters" and "crevices") with minimizers and shocks in the Burgers turbulence, and to introduce a new kind of equipped Airy process for ballistic growth. We dub it the "hairy Airy process" and investigate its statistics numerically. We also identify scaling laws that characterize the ballistic deposition patterns in the bulk: the law of "thinning" of the forest of clusters with increasing height, the law of transversal fluctuations of cluster boundaries, and the size distribution of clusters. The corresponding critical exponents are determined exactly based on the analogy with the Burgers turbulence and simple scaling considerations.
Magic numbers are predicted in wide range of the nuclear chart by the self-consistent mean-field calculations with the M3Y-P6 and P7 semi-realistic $NN$ interactions. The magic numbers are identified by vanishing pair correlations in the spherical Hartree-Fock-Bogolyubov regime. We also identify submagic numbers when energy gain due to the pairing is sufficiently small. It is found that the results with M3Y-P6 well correspond to the known data, apart from a few exceptions. For some of the magic or submagic numbers the prediction differs from that with the Gogny-D1S or D1M interaction. Roles of the tensor force and the spin-isospin channel originating from the one-pion exchange potential are investigated in the $Z$- or $N$-dependence of the shell gap.
Fluctuation dynamics in magnetization plateaux are a relatively poorly explored area in frustrated magnetism. Here we use muon spin relaxation to determine the fluctuation timescale and associated field distribution width in the partial magnetization plateau of Ca3Co2O6. The muon spin relaxation rate has a simple and characteristic field dependence which we model and by fitting to the data at 15 K extract a fluctuation timescale tau = 880(30) ps and a field distribution width Delta = 40.6(3) mT. Comparison with previous results on Ca3Co2O6 suggests that this fluctuation timescale can be associated with short-range, slowly fluctuating magnetic order.