ShantanuT01/DACTYL-Pretraining huggingface dataset:
The surface orientation can have profound effects on the atomic-scale processes of crystal growth, and is essential to such technologies as GaN-based light-emitting diodes and high-power electronics. We investigate the dependence of homoepitaxial growth mechanisms on the surface orientation of a hexagonal crystal using kinetic Monte Carlo simulations. To model GaN metal-organic vapor phase epitaxy, in which N species are supplied in excess, only Ga atoms on a hexagonal close-packed (HCP) lattice are considered. The results are thus potentially applicable to any HCP material. Growth behaviors on c-plane ${(0 0 0 1)}$ and m-plane ${(0 1 \overline{1} 0)}$ surfaces are compared. We present a reciprocal space analysis of the surface morphology, which allows extraction of growth mode boundaries and direct comparison with surface X-ray diffraction experiments. For each orientation we map the boundaries between 3-dimensional, layer-by-layer, and step flow growth modes as a function of temperature and growth rate. Two models for surface diffusion are used, which produce different effective Ehrlich-Schwoebel step-edge barriers, and different adatom diffusion anisotropies on m-plane surfaces. Simulation results in agreement with observed GaN island morphologies and growth mode boundaries are obtained. These indicate that anisotropy of step edge energy, rather than adatom diffusion, is responsible for the elongated islands observed on m-plane surfaces. Island nucleation spacing obeys a power-law dependence on growth rate, with exponents of -0.24 and -0.29 for m- and c-plane, respectively.
A linear dispersive mechanism for error focusing in polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity. Several popular schemes are analyzed and are shown to admit spurious caustics. It is also observed that caustic-free schemes can be defined, like the Crank-Nicolson scheme.
Using the most general model independent form of the effective Hamiltonian, the rare B_s --> \gamma \ell^+ \ell^- decays are studied by taking into account the polarization of the photon. The total and the differential branching ratios for these decays, when photon is in the positive and negative helicity states, are presented. Dependence of these observables on the new Wilson coefficients are studied. It is also investigated the sensitivity of "photon polarization asymmetry" in B_s --> \gamma \ell^+ \ell^- decays to the new Wilson coefficients. It has been shown that all these physical observables are very sensitive to the existence of new physics beyond SM and their experimental measurements can give valuable information about it.
We present a search for CII emission over cosmological scales at high-redshifts. The CII line is a prime candidate to be a tracer of star formation over large-scale structure since it is one of the brightest emission lines from galaxies. Redshifted CII emission appears in the submillimeter regime, meaning it could potentially be present in the higher frequency intensity data from the Planck satellite used to measure the cosmic infrared background (CIB). We search for CII emission over redshifts z=2-3.2 in the Planck 545 GHz intensity map by cross-correlating the 3 highest frequency Planck maps with spectroscopic quasars and CMASS galaxies from the Sloan Digital Sky Survey III (SDSS-III), which we then use to jointly fit for CII intensity, CIB parameters, and thermal Sunyaev-Zeldovich (SZ) emission. We report a measurement of an anomalous emission $\mathrm{I_\nu}=6.6^{+5.0}_{-4.8}\times10^4$ Jy/sr at 95% confidence, which could be explained by CII emission, favoring collisional excitation models of CII emission that tend to be more optimistic than models based on CII luminosity scaling relations from local measurements; however, a comparison of Bayesian information criteria reveal that this model and the CIB & SZ only model are equally plausible. Thus, more sensitive measurements will be needed to confirm the existence of large-scale CII emission at high redshifts. Finally, we forecast that intensity maps from Planck cross-correlated with quasars from the Dark Energy Spectroscopic Instrument (DESI) would increase our sensitivity to CII emission by a factor of 5, while the proposed Primordial Inflation Explorer (PIXIE) could increase the sensitivity further.
We study entanglement dynamics in the nearest-neighbour fermionic chain that is subjected to both DC and AC electric fields. The dynamics gives the well known Bloch oscillations in the DC field case provided that the system size is larger than the Bloch length whereas in the AC field case the entropy is bounded and oscillates with the driving frequency at the points of dynamical localization, and has a logarithmic growth at other points. A combined AC + DC field yields super Bloch oscillations for the system size larger than the super Bloch length which puts a constraint on the device size in a typical non-equilibrium set-up to observe super Bloch oscillations where the device is connected to the leads. Entanglement entropy provides useful signatures for all of these phenomena, and an alternate way to capture the various length scales involved.
We consider far from equilibrium heat transport in chaotic billiard chains with non-interacting charged particles in the presence of non-uniform transverse magnetic field. If half of the chain is placed in a strong magnetic field, or if the strength of the magnetic field has a large gradient along the chain, heat current is shown to be asymmetric with respect to exchange of the temperatures of the heat baths. Thermal rectification factor can be arbitrarily large for sufficiently small temperature of one of the baths.
In their work on `Coxeter-like complexes', Babson and Reiner introduced a simplicial complex $\Delta_T$ associated to each tree $T$ on $n$ nodes, generalizing chessboard complexes and type A Coxeter complexes. They conjectured that $\Delta_T$ is $(n-b-1)$-connected when the tree has $b$ leaves. We provide a shelling for the $(n-b)$-skeleton of $\Delta_T$, thereby proving this conjecture.   In the process, we introduce notions of weak order and inversion functions on the labellings of a tree $T$ which imply shellability of $\Delta_T$, and we construct such inversion functions for a large enough class of trees to deduce the aforementioned conjecture and also recover the shellability of chessboard complexes $M_{m,n}$ with $n \ge 2m-1$. We also prove that the existence or nonexistence of an inversion function for a fixed tree governs which networks with a tree structure admit greedy sorting algorithms by inversion elimination and provide an inversion function for trees where each vertex has capacity at least its degree minus one.
Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy computations of a matched-filtering step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. We address this shortcoming by arranging dictionary atoms in the form of cover tree structures and adopt the corresponding fast approximate nearest neighbour searches to accelerate matched-filtering. For datasets belonging to smooth low-dimensional manifolds cover trees offer search complexities logarithmic in terms of data population. With this motivation we propose an iterative reconstruction algorithm, named CoverBLIP, to address large-size MRF problems where the fingerprint dictionary i.e. discrete manifold of Bloch responses, encodes several intrinsic NMR parameters. We study different forms of convergence for this algorithm and we show that provided with a notion of embedding, the inexact and non-convex iterations of CoverBLIP linearly convergence toward a near-global solution with the same order of accuracy as using exact brute-force searches. Our further examinations on both synthetic and real-world datasets and using different sampling strategies, indicates between 2 to 3 orders of magnitude reduction in total search computations. Cover trees are robust against the curse-of-dimensionality and therefore CoverBLIP provides a notion of scalability -- a consistent gain in time-accuracy performance-- for searching high-dimensional atoms which may not be easily preprocessed (i.e. for dimensionality reduction) due to the increasing degrees of non-linearities appearing in the emerging multi-parametric MRF dictionaries.
For the Schr\"odinger flow from $R^2 \times R^+$ to the 2-sphere $S^2$, it is not known if finite energy solutions can blow up in finite time. We study equivariant solutions whose energy is near the energy of the family of equivariant harmonic maps. We prove that such solutions remain close to the harmonic maps until the blow up time (if any), and that they blow up if and only if the length scale of the nearest harmonic map goes to zero.
The present work considers a plane shock front propagating along a cylindrical jet. Electrons experience the diffusive shock acceleration around the shock front, and subsequently drift away into the downstream flow in which they emit most of their energy. Assuming a proper boundary condition at the interface between the shock zone and the downstream zone, we solve the transport equation for the electrons in the downstream flow zone, where the combined effects of escape, synchrotron and IC cooling in the Thomson regime are taken into account. Using the electron spectrum obtained in this manner we calculate the multi-wavelength spectral energy distribution of Mrk 501 in the synchrotron self-Compton scenario. We check numerically if the Klein-Nishina cross-section could be approximated to the Thomsom regime. We consider whether the model results yield physically reasonable parameters, and further discuss some of implications of the model results. It suggests that the process of diffusive shock acceleration operates in the outflow of Mrk 501.
Let X be a complete toric variety and let Y be a smooth projective variety with Picard number one. We prove that, if there exists a surjective morphism from X to Y, then Y is a projective space.
This is the first in a series of papers in which we describe and report the analysis of a large survey of Herbig Ae/Be stars in circular spectropolarimetry. Using the ESPaDOnS and Narval high-resolution spectropolarimeters at the Canada-France-Hawaii and Bernard Lyot Telescopes, respectively, we have acquired 132 circularly-polarised spectra of 70 Herbig Ae/Be stars and Herbig candidates. The large majority of these spectra are characterised by a resolving power of about 65,000, and a spectral coverage from about 3700 ang to 1 micron. The peak SNR per CCD pixel ranges from below 100 (for the faintest targets) to over 1000 (for the brightest). The observations were acquired with the primary aim of searching for magnetic fields in these objects. However, our spectra are suitable for a variety of other important measurements, including rotational properties, variability, binarity, chemical abundances, circumstellar environment conditions and structure, etc. In this first paper, we describe the sample selection, the observations and their reduction, and the measurements that will comprise the basis of much of our following analysis. We describe the determination of fundamental parameters for each target. We detail the Least-Squares Deconvolution that we have applied to each of our spectra, including the selection, editing and tuning of the LSD line masks. We describe the fitting of the LSD Stokes I profiles using a multi-component model that yields the rotationally-broadened photospheric profile (providing the projected rotational velocity and radial velocity for each observation) as well as circumstellar emission and absorption components. Finally, we diagnose the longitudinal Zeeman effect via the measured circular polarisation, and report the longitudinal magnetic field and Stokes V Zeeman signature detection probability. As an appendix, we provide a detailed review of each star observed.
The Devasthal Fast Optical Telescope (DFOT) is a 1.3 meter aperture optical telescope, recently installed at Devasthal, Nainital. We present here the first results using an \Ha filter with this telescope on a Wolf-Rayet dwarf galaxy Mrk 996. The instrumental response and the \Ha sensitivity obtained with the telescope are $(3.3 \pm 0.3)\times 10^{-15} (erg s^{-1} cm^{-2})/(counts s^{-1})$ and $7.5\times10^{-17} erg s^{-1} cm^{-2} arcsec^{-2}$ respectively. The \Ha flux and the equivalent width for Mrk~996 are estimated as $(132 \pm 37)\times 10^{-14} erg s^{-1} cm^{-2}$ and $\sim$96 $\mathring{A}$ respectively. The star formation rate is estimated as $0.4\pm0.1 M_\odot$yr$^{-1}$. Mrk~996 deviates from the radio-FIR correlation known for normal star forming galaxies with a deficiency in its radio continuum. The ionized gas as traced by \Ha emission is found in a disk shape which is misaligned with respect to the old stellar disk. This misalignment is indicative of a recent tidal interaction in the galaxy. We believe that galaxy-galaxy tidal interaction is the main cause of the WR phase in Mrk~996.
A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence that is weaker than exchangeability, but is equivalent to exchangeability for stationary sequences. In this article we extend this notion to families of sequences. Paralleling the extension from exchangeability to partial exchangeability in the sense of de Finetti, we propose a notion of partially c.i.d. dependence, that is equivalent to partial exchangeability for stationary processes. Partially c.i.d. families of sequences preserve attractive limit properties of partial exchangeability, and are asymptotically partially exchangeable. Moreover, we provide strong laws of large numbers and two central limit theorems. Our focus is on the asymptotic agreement of predictions and empirical means, which lies in the foundations of Bayesian statistics. Natural examples are interacting randomly reinforced processes satisfying certain conditions on the reinforcement.
The kinetics of negatively charged kaon condensation in the early stages of a newly born neutron star is considered. The thermal kaon process, in which kaons are thermally produced by nucleon-nucleon collisions, is found to be dominant throughout the equilibration process. Temporal changes of the order parameter of the condensate and the number densities of the chemical species are obtained from the rate equations, which include the thermal kaon reactions as well as the kaon-induced Urca and the modified Urca reactions. It is shown that the dynamical evolution of the condensate is characterized by three stages: the first, prior to establishment of a condensate, the second, during the growth and subsequent saturation of the condensate, and the third, near chemical equilibrium. The connection between the existence of a soft kaon mode and the instability of the noncondensed state is discussed. Implications of the nonequilibrium process on the possible delayed collapse of a protoneutron star are also mentioned.
We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume under this condition. They extend the concept of 2D polyominoes inscribed in a rectangle defined in a previous work. Using their geometric structure and elementary combinatorial arguments, we construct generating functions of minimal 3D polyominoes in the form of rational functions. We also obtain a number of exact formulas and recurrences for sub-families of these polyominoes.
The Jeans criterion for the minimum self-gravitational condensation scale is extended to include the possibility of condensation on non-acoustic density nuclei at Schwarz scales, where structure formation begins in the plasma epoch at proto-supercluster masses about 10,000 years after the Big Bang, decreasing to galaxy masses at 300,000 years. Then the plasma universe became relatively inviscid gas and condensed to 10^23-26 kg "primordial fog particle" (PFP) masses. Baryonic dark matter by this theory should be mostly non-aggregated PFPs that persist in galactic halos. Schild (1996) suggests from quasar Q0957+561 microlensing that "rogue planets" are "likely to be the missing mass" of the lens galaxy. Non-baryonic dark matter composed of weakly interacting massive particles (WIMPs) should condense slowly at large viscous Schwarz scales to form galaxy supercluster halos, and massive galaxy cluster halos as observed by Tyson and Fischer (1995) for the rich galaxy cluster Abel 1689.
It is well known that in a braneworld model, the localization of fermions on lower dimensional submanifold (say a TeV 3-brane) is governed by the gravity in the bulk which also determines the corresponding phenomenology on the brane. Here we consider a five dimensional warped spacetime where the bulk geometry is governed by higher curvature like F(R) gravity. In such a scenario, we explore the role of higher curvature terms on the localization of bulk fermions which in turn determines the effective radion-fermion coupling on the brane. Our result reveals that for appropriate choices of the higher curvature parameter, the profiles of the massless chiral modes of the fermions may get localized near TeV brane while that for massive Kaluza-Klein (KK) fermions localize towards the Planck brane. We also explore these features in the dual scalar-tensor model by appropriate transformations. The localization property turns out to be identical in both the models. This rules out the possibility of any signature of massive KK fermions in TeV scale collider experiments due to higher curvature gravity effects.
The electrical conductivity is calculated for regular inhomogeneous two component isotropic medium in which droplets of one phase with conductivity sigma_2 are embedded in another, with conductivity sigma_1. An expression is formulated which can be used in many different situations, and is of particular relevance in the case where the relative proportion of the components is temperature dependent and varies over a wide range. The behavior of effective conductivity depends on the spatial arrangements and the shape of the inclusions.
We investigate the indirect interaction between two isolated impurities in a Luttinger liquid described by a microscopic lattice model. To treat the electron-electron interaction U the functional renormalization group method is used. For comparison we also study the U=0 case. We find that for a wide range of impurity parameters the impurity interaction V_{12} as a function of their separation r oscillates with decaying amplitude between being attractive and repulsive. For half-filling of the band and in a crossover regime between weak and strong impurities the interaction becomes purely attractive. For U=0 and independent of the impurity strength the amplitude of the interaction energy falls off as 1/r. For U>0 the decay for small separations and weak to intermediate impurities is governed by a U dependent exponent larger than -1, which crosses over to -1 for large r. The crossover scale depends on the impurity strength and U. We present simple pictures which explain our results in the limits of weak and strong impurities. We finally also consider attractive interactions U<0.
We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging length scale near a critical point. Picking target clusters with probability proportional to their mass leads to a runaway compact cluster. Choosing all clusters equally leads to a continuous transition in a new universality class for the square lattice, while the transition on the triangular lattice has the same critical exponents as ordinary percolation.
In this note we consider Diophantine equations of the form \begin{equation*} a(x^p-y^q) = b(z^r-w^s), \quad \mbox{where}\quad \frac{1}{p}+\frac{1}{q}+\frac{1}{r}+\frac{1}{s}=1, \end{equation*} with even positive integers $p,q,r,s$. We show that in each case the set of rational points on the underlying surface is dense in the Zariski topology. For the surface with $(p,q,r,s)=(2,6,6,6)$ we prove density of rational points in the Euclidean topology. Moreover, in this case we construct infinitely many parametric solutions in coprime polynomials. The same result is true for $(p,q,r,s)\in\{(2,4,8,8), (2,8,4,8)\}$. In the case $(p,q,r,s)=(4,4,4,4)$, we present some new parametric solutions of the equation $x^4-y^4=4(z^4-w^4)$.
This paper is devoted to the asymptotic analysis of the optimal Sobolev constants in the semiclassical limit and in any dimension. We combine semiclassical arguments and concentration-compactness estimates to tackle the case when an electromagnetic field is added as well as a smooth boundary carrying a Robin condition. As a byproduct of the semiclassical strategy, we also get exponentially weighted localization estimates of the minimizers.
The nuclear star cluster surrounding the massive black hole at the Galactic Centre consists of young and old stars, with most of the stellar mass in an extended, cuspy distribution of old stars. The compact cluster of young stars was probably born in situ in a massive accretion disc around the black hole. We investigate the effect of the growing gravity of the disc on the orbits of the old stars, using an integrable model of the deformation of a spherical star cluster with anisotropic velocity dispersions. A formula for the perturbed phase space distribution function is derived using linear theory, and new density and surface density profiles are computed. The cusp undergoes a spheroidal deformation with the flattening increasing strongly at smaller distances from the black hole; the intrinsic axis ratio ~ 0.8 at ~ 0.15 pc. Stellar orbits are deformed such that they spend more time near the disc plane and sample the dense inner parts of the disc; this could result in enhanced stripping of the envelopes of red giant stars. Linear theory accounts only for orbits whose apsides circulate. The non-linear theory of adiabatic capture into resonance is needed to understand orbits whose apsides librate. The mechanism is a generic dynamical process, and it may be common in galactic nuclei.
We show that the von Neumann's algorithm of reduction (i.e. the algorithm of calculating the density matrix of the observable subsystem from the density matrix of the closed quantum system) corresponds to the special approximation at which the unobservable subsystem is supposed to be in the steady state of minimum information (infinite temperature). We formulate the generalized algorithm of reduction that includes as limiting cases the von Neumann's reduction and the self-congruent correlated reduction most corresponding to the quantum nondemolition measurement. We demonstrate the correlation in dynamics of subsystems with exactly soluble models of quantum optics: 1) about the dynamics of a pair of interacting two-level atoms, and 2) about the dynamics of a two-level atom interacting with a single-mode resonant field.