ShantanuT01/DACTYL-Pretraining huggingface dataset:
Study on the electronic transport of a large scale two dimensional system by the transfer matrix method (TMM) based on the Sch\"{o}rdinger equation suffers from the numerical instability. To address this problem, we propose a renormalized transfer matrix method (RTMM) by setting up a set of linear equations from U times of multiplication of traditional transfer matrix (U=N/S}with N and S being the atom number of length and the transfer step), and smaller S is required for wider systems. Then we solve the above linear equations by Gauss elimination method and further optimize to reduce the computational complexity from O(U^3M^3) to O(UM^3), in which M is the atom number of the width. Applying RTMM, we study transport properties of large scale pure and long-range correlated disordered armchair graphene nanoribbon (AGR) (carbon atoms up to 10^6 for pure case) between quantum wire contacts. As for pure AGR, the conductance is superlinear with the Fermi energy and the conductance is linear with the width while independent of the length, showing characteristics of ballistic transport. As for disordered AGR with long-range correlation, there is metal-insulator transition induced by the correlation strength of disorder. It is straightforward to extend RTMM to investigate transport in large scale system with irregular structure.
In this article we demonstrate the injection locking of recently demonstrated spintronic feedback nano oscillator to microwave magnetic fields at integers as well fractional multiples of its auto oscillation frequency. Feedback oscillators have delay as a new degree of freedom which is absent for spin-transfer torque based oscillators, which gives rise to side peaks along with a main peak. We show that it is also possible to lock the oscillator on its side band peaks, which opens a new avenue to phase locked oscillators with large frequency differences. We observe that for low driving fields, side band locking improves the quality factor of the main peak, whereas for higher driving fields the main peak is suppressed. Further, measurements at two field angles provide some insight into the role of symmetry of oscillation orbit in determining the fractional locking.
The paper deals with cosmological solutions describing different phases of the Universe for the homogeneous and isotropic FLRW model of the Universe with torsion. Normally, torsion field is not suitable for maximally symmetric space time model. However, one may use a specific profile of vectorial torsion field, derived from a scalar function. By proper choices of the torsion scalar function, it is shown that a continuous cosmic evolution starting from the emergent scenario to the present late time acceleration is possible. Also thermodynamics of the system is analyzed and equivalence with Einstein gravity is discussed.
We study dual geometries to a deformed ABJM model with spatially dependent source functions at finite temperature. These source functions are proportional to the mass function $m(x)= m_0 \sin k x$ and its derivative $m'(x)$. As dual geometries, we find hairy black branes and AdS solitons corresponding to deconfinement phase and confining phase of the dual field theory, respectively. It turns out that the hairy AdS solitons have lower free energy than the black branes when the Hawking temperature is smaller than the confining scale. Therefore the dual system undergoes the first order phase transition. Even though our study is limited to the so-called Q-lattice ansatz, the solution space contains a set of solutions dual to a supersymmetric mass deformation. As a physical quantity to probe the confining phase, we investigate the holographic entanglement entropy and discuss its behavior in terms of modulation effect.
The structure of the broad emission line region (BLR) in active galactic nuclei (AGN) remains unclear. We test in this paper a flattened configuration model for BLR. The virial theorem, by taking into account the disc shape of BLR, allows us to get a direct connection between the mass of a supermassive black hole (SMBH) and the inclination angle of the accretion flow. The inclination angle itself is derived from the spectropolarimetric data on broad emission lines using the theory for the generation of polarized radiation developed by Sobolev and Chandrasekhar. As the result, the new estimates of SMBH masses in AGN with measured polarization of BLR are presented. It is crucial that the polarimetric data allow also to determine the value of the virial coefficient that is essential for determining SMBH masses.
The mass-luminosity relation for late-type stars has long been a critical tool for estimating stellar masses. However, there is growing need for both a higher-precision relation and a better understanding of systematic effects (e.g., metallicity). Here we present an empirical relationship between Mks and mass spanning $0.075M_\odot<M<0.70M_\odot$. The relation is derived from 62 nearby binaries, whose orbits we determine using a combination of Keck/NIRC2 imaging, archival adaptive optics data, and literature astrometry. From their orbital parameters, we determine the total mass of each system, with a precision better than 1% in the best cases. We use these total masses, in combination with resolved Ks magnitudes and system parallaxes, to calibrate the mass-Mks relation. The result can be used to determine masses of single stars with a precision of 2-3%, which we confirm by a comparison to dynamical masses from the literature. The precision is limited by scatter around the best-fit relation beyond mass uncertainties, perhaps driven by intrinsic variation in the mass-Mks relation or underestimated measurement errors. We find the effect of [Fe/H] on the mass-Mks relation is likely negligible for metallicities in the Solar neighborhood (0.0+/-2.2% change in mass per dex change in [Fe/H]). This weak effect is consistent with predictions from the Dartmouth Stellar Evolution Database, but inconsistent with those from MESA Isochrones and Stellar Tracks. A sample of binaries with a wider range of abundances will be required to discern the importance of metallicity in extreme populations (e.g., in the Galactic Halo or thick disk).
We study negative association (NA) for mixed sampled point processes and show that NA holds for such processes if the random number of points of them fulfills ULC property. We connect NA property of point processes with dcx dependence ordering and show some consequences of it for mixed sampled and determinantal point processes. Some applications illustrate general theory.
The magnetic field opens a gap in the edge state spectrum of two-dimensional topological insulators thereby destroying protection of these states against backscattering. To relate properties of this gap to parameters of the system and to study dynamics of electrons in edge states in the presence of inhomogeneous potentials, the effective Hamiltonian theory is developed. Using this analytical theory, quantum-mechanical problems of edge-state electron transmission through potential steps and barriers, and of motion in constant electric field are considered. The influence of magnetic field on the resistance of two-dimensional topological insulators based on HgTe quantum wells is discussed together with comparison to experimental data.
We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition on the data to be null controllable, i.e., can be driven to the zero state. We also show that the validity of this condition allows the states to be stirred to each other. If the condition is not satisfied, one can move from one state to another with the help of a simple shear external magnetic force.
We calculate determinants of weighted sums of reflections and of (nested) commutators of reflections. The results obtained generalize the Kirchhoff's matrix-tree theorem and the matrix-3-hypertree theorem by G.\,Massbaum and A.\,Vaintrob.
We show the existence of surfaces of degree $d$ in $\dP^3(\dC)$ with approximately ${3j+2\over 6j(j+1)} d^3$ singularities of type $A_j, 2\le j\le d-1$. The result is based on Chmutov's construction of nodal surfaces. For the proof we use plane trees related to the theory of Dessins d'Enfants. Our examples improve the previously known lower bounds for the maximum number $\mu_{A_j}(d)$ of $A_j$-singularities on a surface of degree $d$ in most cases. We also give a generalization to higher dimensions which leads to new lower bounds even in the case of nodal hypersurfaces in $\dP^n, n\ge5$. To conclude, we work out in detail a classical idea of B. Segre which leads to some interesting examples, e.g. to a sextic with 36 cusps.
Zinc is a useful surrogate element for measuring Fe/H as, unlike iron, it is not depleted in the gas phase media. Zn/H and O/Zn ratios have been derived using the [Zn IV] emission line at 3.625um for a sample of nine Galactic planetary nebulae, seven of which are based upon new observations using the VLT. Based on photoionization models, O/O++ is the most reliable ionisation correction factor for zinc that can readily be determined from optical emission lines, with an estimated accuracy of 10% or better for all targets in our sample. The majority of the sample is found to be sub-solar in [Zn/H]. [O/Zn] in half of the sample is found to be consistent with Solar within uncertainties, whereas the remaining half are enhanced in [O/Zn]. [Zn/H] and [O/Zn] as functions of Galactocentric distance have been investigated and there is little evidence to support a trend in either case.
The canonical observation mode for IACT gamma-ray observations employs four discrete pointings in the cardinal directions (the "wobble" mode). For the VERITAS Observatory, the target source is offset by 0.5-0.7 degrees from the camera center, and the observation lasts 20 minutes. During January/February of 2011, the VERITAS Observatory tested a new "orbit" observation mode, where the target source is continuously rotated around the camera center at a fixed radial offset and constant angular velocity. This mode of observation may help better estimate the cosmic ray background across the field of view, and will also reduce detector dead-time between the discrete 20 minute runs. In winter 2011, orbit mode observations where taken on the Crab Nebula and Mrk 421. In this paper we present the analysis of these observations, and describe the potential applications of orbit mode observations for diffuse (extended) sources as well as GRBs.
We present new spectropolarimetric data for WR 42 collected over 6 months at the 11-m Southern African Large Telescope (SALT) using the Robert Stobie Spectrograph.
It is expected that, within the next three years, the determination of the CKM matrix elements with the least theoretical uncertainty will arise from the measurements of CP violation in B_d --> J/\psi K_S decays and from Bs-Bsbar mixing. If there is significant new physics in Bs-Bsbar mixing, then those experiments will not yield the correct values for the CKM matrix elements. As a result, a qualitative signal of new physics may appear in the CP violation of decays like B_d --> pi+ pi-.
The ground-state magnetic response of fullerene molecules with up to 36 vertices is calculated, when spins classical or with magnitude $s=\frac{1}{2}$ are located on their vertices and interact according to the nearest-neighbor antiferromagnetic Heisenberg model. The frustrated topology, which originates in the pentagons of the fullerenes and is enhanced by their close proximity, leads to a significant number of classical magnetization and susceptibility discontinuities, something not expected for a model lacking magnetic anisotropy. This establishes the classical discontinuities as a generic feature of fullerene molecules irrespective of their symmetry. The largest number of discontinuities have the molecule with 26 sites, four of the magnetization and two of the susceptibility, and an isomer with 34 sites, which has three each. In addition, for several of the fullerenes the classical zero-field lowest energy configuration has finite magnetization, which is unexpected for antiferromagnetic interactions between an even number of spins and with each spin having the same number of nearest-neighbors. The molecules come in different symmetries and topologies and there are only a few patterns of magnetic behavior that can be detected from such a small sample of relatively small fullerenes. Contrary to the classical case, in the full quantum limit $s=\frac{1}{2}$ there are no discontinuities for a subset of the molecules that was considered. This leaves the icosahedral symmetry fullerenes as the only ones known supporting ground-state magnetization discontinuities for $s=\frac{1}{2}$. It is also found that a molecule with 34 sites has a doubly-degenerate ground state when $s=\frac{1}{2}$.
We present a near-infrared study of the Seyfert 2 galaxy NGC\,6300, based on subarcsecond images and long slit spectroscopy obtained with Flamingos-2 at Gemini South. We have found that the peak of the nuclear continuum emission in the $K_s$ band and the surrounding nuclear disk are 25\,pc off-center with respect to the center of symmetry of the larger scale circumnuclear disk, suggesting that this black hole is still not fixed in the galaxy potential well. The molecular gas radial velocity curve yields a central black hole upper mass estimation of $M_{SMBH}^{upper}=(6\pm 2) \times 10^{7}\,\Msun$. The Pa$\beta$ emission line has a strongly asymmetric profile with a blueshifted broad component that we associate with a nuclear ionized gas outflow. We have found in the $K_s$-band spectra that the slope of the continuum becomes steeper with increasing radii, which can be explained as the presence of large amounts of hot dust not only in the nucleus but also in the circumnuclear region up to $r=27$\,pc. In fact, the nuclear red excess obtained after subtracting the stellar contribution resembles to that of a blackbody with temperatures around 1200\,K. This evidence supports the idea that absorbing material located around the nucleus, but not close enough to be the torus of the unified model, could be responsible for at least part of the nuclear obscuration in this Seyfert 2 nucleus.
Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Preparing the mechanical resonator in non-classical states enables an optomechanical Stern-Gerlach interferometer. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, we recover single photon and two-photon interference via a classically controlled beam splitter. The visibility of the two-photon interference is particularly sensitive to coherent excitations in the mechanical resonator and this could form the basis of an optically transduced weak-force sensor.
We present a method of filter diagonalization for shell-model calculations. This method is based on the Sakurai and Sugiura (SS) method, but extended with help of the shifted complex orthogonal conjugate gradient (COCG) method. A salient feature of this method is that it can calculate eigenvalues and eigenstates in a given energy interval. We show that this method can be an alternative to the Lanczos method for calculating ground and excited states, as well as spectral strength functions. With an application to the $M$-scheme shell-model calculations we demonstrate that several inherent problems in the widely-used Lanczos method can be removed or reduced.
We define the model of two-dimensional random interlacements using simple random walk trajectories conditioned on never hitting the origin, and then obtain some properties of this model. Also, for random walk on a large torus conditioned on not hitting the origin up to some time proportional to the mean cover time, we show that the law of the vacant set around the origin is close to that of random interlacements at the corresponding level. Thus, this new model provides a way to understand the structure of the set of late points of the covering process from a microscopic point of view.
A quantity that promises to reveal important information on perturbative and non-perturbative QCD dynamics is the azimuthal decorrelation between jets in different hard processes. In order to access this information fixed-order NLO predictions need to be supplemented by resummation of logarithmic terms which are large in the region where the jets are nearly back-to-back in azimuth. In the present letter we carry out this resummation to next-to--leading logarithmic accuracy explaining the important role played by the recombination scheme in general resummations for such jet observables.
$\newcommand{\OO}[1]{\mathcal{O}_{#1}}\newcommand{\GG}{\mathcal{G}}\newcommand{\End}{\mathrm{End}}\newcommand{\O}{\mathcal{O}}$Let $K/F$ be a quadratic extension of non-Archimedean local fields of characteristic not equal to 2, with rings of integers denoted by $\OO K$ and $\OO F$. We consider a formal $\OO F$-module $\GG$, over a discrete valuation ring $\OO W$ with an uniformizer $\varpi$, with extra endomorphisms by a subring $\O$ of $\OO K$, and the height of its reduction $\GG_0=\GG\otimes \OO W/\varpi$ is 2. The endomorphism ring of $\GG_n=\GG\otimes \OO W/\varpi^{n+1}$ is a subring between $\OO s$ and $\OO D=\End(\GG_0)$. We will determine them explicitly. This result was previously proved by Gross and Keating. Their treatment is the formal cohomology theory. We will give another proof using the intersection formula of CM cycles in Lubin-Tate deformation spaces.
We present a formalism of distorted wave impulse approximation (DWIA) for analyzing spin observables in nucleon inelastic and charge exchange reactions leading to the continuum. It utilizes response functions calculated by the continuum random phase approximation (RPA), which include the effective mass, the spreading widths and the \Delta degrees of freedom. The Fermi motion is treated by the optimal factorization, and the non-locality of the nucleon-nucleon t-matrix by an averaged reaction plane approximation. By using the formalism we calculated the spin-longitudinal and the spin-transverse cross sections, ID_q and ID_p, of 12C, 40Ca (\vec{p},\vec{n}) at 494 and 346 MeV. The calculation reasonably reproduced the observed ID_q, which is consistent with the predicted enhancement of the spin-longitudinal response function R_L. However, the observed ID_p is much larger than the calculated one, which was consistent with neither the predicted quenching nor the spin-transverse response function R_T obtained by the (e,e') scattering. The Landau-Migdal parameter g'_N\Delta for the N\Delta transition interaction and the effective mass at the nuclear center m^*(r=0) are treated as adjustable parameters. The present analysis indicates that the smaller g'_{N\Delta}(\approx 0.3) and m^*(0) \approx 0.7 m are preferable. We also investigate the validity of the plane wave impulse approximation (PWIA) with the effective nucleon number approximation for the absorption, by means of which R_L and R_T have conventionally been extracted.
According to several reports published by worldwide organisations, thousands of pedestrians die in road accidents every year. Due to this fact, vehicular technologies have been evolving with the intent of reducing these fatalities. This evolution has not finished yet since, for instance, the predictions of pedestrian paths could improve the current Automatic Emergency Braking Systems (AEBS). For this reason, this paper proposes a method to predict future pedestrian paths, poses and intentions up to 1s in advance. This method is based on Balanced Gaussian Process Dynamical Models (B-GPDMs), which reduce the 3D time-related information extracted from keypoints or joints placed along pedestrian bodies into low-dimensional spaces. The B-GPDM is also capable of inferring future latent positions and reconstruct their associated observations. However, learning a generic model for all kind of pedestrian activities normally provides less ccurate predictions. For this reason, the proposed method obtains multiple models of four types of activity, i.e. walking, stopping, starting and standing, and selects the most similar model to estimate future pedestrian states. This method detects starting activities 125ms after the gait initiation with an accuracy of 80% and recognises stopping intentions 58.33ms before the event with an accuracy of 70%. Concerning the path prediction, the mean error for stopping activities at a Time-To-Event (TTE) of 1s is 238.01mm and, for starting actions, the mean error at a TTE of 0s is 331.93mm.
We discuss how we remove a huge discrepancy between the theory of a cosmological constant, due to the zero-point energies of matter fields, and the observation. The technique of dimensional regularization plays a decisive role. We eventually reach the desired behavior of the vacuum densities falling off like t^{-2}, allowing us to understand how an extremely small result comes about naturally. As a price, however, the zero-point energy vacuum fails to act as a true cosmological constant. Its expected role responsible for the observed accelerating universe is then to be inherited by the gravitational scalar field, dark energy, as we suggest in the scalar-tensor theory.
An elementary constituent-quark (CQ) model of mesons was previously presented. In this paper, we continue research into a study of the baryons in the constituent-quark model. Mac Gregor proposed a comprehensive model of elementary particles for which both mesons and baryons shared common mass-band structure in quantized units of m = 70 MeV, B= 140 MeV and X = 420 MeV. A review of the baryon data is under taken for comparison with the CQ model. It is shown in this paper that baryons possess an isospin I related to the mass quantum m = 70 MeV and to the B = 140 MeV quantum (or the mass of the pion). In order to establish a consistency with the quark model of Gell-Mann, we identify the SU(3) baryon decuplet as a standard feature to be maintained with only slight changes to the constituent-quark masses. By insisting on the J = 3/2, P-states of the SU(3) baryon decuplet to be in the same CQ excitation states, we are lead to establish baryon cores in the P-states with J = 1/2. Core corrections to Mac Gregor's CQ model of baryons are presented. Exact shell structure is found among all the baryons regardless of isospin as evidenced in the data from the Particle Data Group listing. New baryons are predicted to exist.
Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial coordinates the outward movement of the event horizon (``slice sucking'') and the unbounded growth there of the radial metric component (``slice wrapping'') are analyzed. For the overall slice stretching, very similar late time behavior is found when comparing with maximal slicing. Thus, the intuitive argument that attributes slice stretching to singularity avoidance is incorrect.
We show that h*-vectors of alcoved polytopes P in R^n (of Lie type A) are unimodal if they contain interior lattice points and their facets have lattice distance 1 to the set of interior lattice points. The maximal possible such distance for general alcoved polytopes is shown to be dim(P)-1. A secondary purpose of the paper is to serve as a guide to previous work surrounding unimodality of h*-vectors of alcoved polytopes and related questions.