ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have performed a detailed analysis of the electron temperature and density in the the Ring Nebula using the calibrated HST WFC3 images described in the preceding paper. The electron temperature (Te) determined from [N II] and [O III] rises slightly and monotonically towards the central star. The observed equivalent width (EW) in the central region indicates that Te rises as high as 13000 K. In contrast, the low EW's in the outer regions are largely due to scattered diffuse Galactic radiation by dust. The images allowed determination of unprecedented small scale variations in Te. These variations indicate that the mean square area temperature fluctuations are significantly higher than expected from simple photoionization. The power producing these fluctuations occurs at scales of less than 3.5E15 cm. This scale length provides a strong restriction on the mechanism causing the large t^2 values observed.
The perturbative renormalization of the Ginzburg-Landau model is reconsidered based on the Feynman diagram technique. We derive renormalization group (RG) flow equations, exactly calculating all vertices appearing in the perturbative renormalization of the phi^4 model up to the epsilon^3 order of the epsilon-expansion. In this case, the phi^2, phi^4, phi^6, and phi^8 vertices appear. All these vertices are relevant. We have tested the expected basic properties of the RG flow, such as the semigroup property. Under repeated RG transformation R_s, appropriately represented RG flow on the critical surface converges to certain s-independent fixed point. The Fourier-transformed two-point correlation function G(k) has been considered. Although the epsilon-expansion of X(k)=1/G(k) is well defined on the critical surface, we have revealed an inconsistency of the perturbative method with the exact rescaling of X(k), represented as an expansion in powers of k at k --> 0. We have discussed also some aspects of the perturbative renormalization of the two-point correlation function slightly above the critical point. Apart from the epsilon-expansion, we have tested and briefly discussed also a modified approach, where the phi^4 coupling constant u is the expansion parameter at a fixed spatial dimensionality d.
We study the thermalization dynamics of one-dimensional diatomic lattices (which represents the simplest system possessing multi-branch phonons), exemplified by the famous Fermi-Pasta-Ulam-Tsingou (FPUT)-$\beta$ and the Toda models. Here we focus on how the system relaxes to the equilibrium state when part of highest-frequency optical modes are initially excited, which is called the anti-FPUT problem comparing with the original FPUT problem (low frequency excitations of the monatomic lattice). It is shown numerically that the final thermalization time $T_{\rm eq}$ of the diatomic FPUT-$\beta$ chain depends on whether its acoustic modes are thermalized, whereas the $T_{\rm eq}$ of the diatomic Toda chain depends on the optical ones; in addition, the metastable state of both models have different energy distributions and lifetimes. Despite these differences, in the near-integrable region, the $T_{\rm eq}$ of both models still follows the same scaling law, i.e., $T_{\rm eq}$ is inversely proportional to the square of the perturbation strength. Finally, comparisons of the thermalization behavior between different models under various initial conditions are briefly summarized.
This works presents the theoretical study on several correlation integrals of the capacitance transients of the deep levels. The deconvolution of the transient signals was the major subject of the number of methods referred to under the common name as the Deep Level Transient Spectroscopy methods. In general the separation of the overlapping exponential decays C(t) does not provide a unique solution, so the detection of the closely spaced deep levels by these transients should base mainly on the temperature dependence C(T), not only on the C(t). The results show that the average emission factor en is obtainable directly from various correlation integrals of the capacitance transients and the average activation energy E of the deep levels is detectable via the shift operators of the transients according to the temperature. A new scanning technique is suggested.
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the formulation is exact. An attractive feature of this approach is that it transparently shows how the geometrical properties of the continuous space are preserved. In the study of the non-perturbative regime of QFT, fuzzy spaces provide a possible alternative to the lattice as a regularisation method. The thesis is divided into two parts. We perform Monte Carlo simulations of a $\lambda \phi^4$ theory on a 3-dimensional Euclidean space. We identify the phase diagram of this model. In addition to the usual disordered and uniform ordered phases we find a third phase of non-uniform ordering. This indicates the existence of the phenomenon called UV-IR mixing in the strong coupling regime. Second we present a geometrical analysis of the scalar field theory on a 4-dimensional fuzzy sphere, S4_F. Nevertheless a fuzzy version of S4 cannot be achieved by quantisation of the classical space. The problem is circumvented by defining a scalar theory on a larger space, CP3 which is 6-dimensional. It includes degrees of freedom related to S^4 plus others beyond S4. Those extra degrees of freedom are dynamically suppressed through a probabilistic method. The analysis of the geometrical structures allows us to interpret this procedure as a Kaluza-Klein reduction of CP3 to S4.
Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we introduce the notion of solutions with a prevailing mode for the nonlinear evolution beam equation $$ u_{tt} + u_{xxxx} + f(u)= g(x, t) $$ in bounded space-time intervals. We give a new definition of instability for these particular solutions, based on the loss of energy concentration on their prevailing mode. We distinguish between two different forms of energy transfer, one physiological (unavoidable and depending on the nonlinearity) and one due to the insurgence of instability. We then prove a theoretical result allowing to reduce the study of this kind of infinite-dimensional stability to that of a finite-dimensional approximation. With this background, we study the occurrence of instability for three different kinds of nonlinearities $f$ and for some forcing terms $g$, highlighting some of their structural properties and performing some numerical simulations.
Chemical tagging has great promise as a technique to unveil our Galaxy's history. Grouping stars based on their similar chemistry can establish details of the star formation and merger history of the Milky Way. With precise measurements of stellar chemistry, chemical tagging may be able to group together stars born from the same gas cloud, regardless of their current positions and kinematics. Successfully tagging these birth clusters requires high quality chemical space information and a good cluster-finding algorithm. To test the feasibility of chemical tagging on data from current and upcoming spectroscopic surveys, we construct a realistic set of synthetic clusters, creating both observed spectra and derived chemical abundances for each star. We use Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to group stars based on their spectra or abundances; these groups are matched to input clusters and are found to be highly homogeneous and complete. The percentage of clusters with more than 10 members recovered is 40% when tagging on abundances with uncertainties achievable with current techniques. Based on our fiducial model for the Milky Way, we predict recovering over 600 clusters with at least 10 observed members and 70% membership homogeneity in a sample similar to the APOGEE survey. Tagging larger surveys like the GALAH survey and the future Milky Way Mapper in SDSS V could recover tens of thousands of clusters at high homogeneity. Access to so many unique co-eval clusters will transform how we understand the star formation history and chemical evolution of our Galaxy.
Inspired by blockchains, we introduce a dynamically growing model of rooted Directed Acyclic Graphs (DAGs) referred to as the asynchronous composition model, subject to i.i.d. random delays $(\xi_t)$ with finite mean. The new vertex at time $t$ is connected to vertices chosen from the graph $G_{(t-\xi_t)_+}$ according to a construction function $f$ and the graph is updated by taking union with the graph $G_{t-1}$. This process corresponds to adding new blocks in a blockchain, where the delays arise due to network communication. The main question of interest is the end structure of the asynchronous limit of the graph sequence as time increases to infinity.   We consider the following construction functions of interest, a) Nakamoto construction $f_{\mathrm{Nak}}$, in which a vertex is uniformly selected from those furthest from the root, resulting in a tree, and b) mixture of construction functions $(f_k)_{1\le k\le \infty}$, where in $f_k$ a random set of $k$ leaves (all if there are less than $k$ in total) is chosen without replacement. The main idea behind the analysis is decoupling the time-delay process from the DAG process and constructing an appropriate regenerative structure in the time-delay process giving rise to Markovian behavior for a functional of the DAG process. We establish that the asynchronous limits for $f_\mathrm{Nak}, (f_k)_{k \ge 2}$, and any non-trivial mixture $f$ are one-ended, while the asynchronous limit for $f_1$ has infinitely many ends, almost surely. We also study fundamental growth properties of the longest path for the sequence of graphs for $f_\mathrm{Nak}$. In addition, we prove a phase transition on the (time and sample-path dependent) probability of choosing $f_1$ such that the asynchronous limit either has one or infinitely many ends. Finally, we show that the construction $f_\infty$ is an appropriate limit of the $(f_k)_k$.
As a test of rotationally-induced mixing causing the well-known Li dip in older mid-F dwarfs in the local Galactic disk, we utilize high-resolution and -S/N Keck/HIRESspectroscopy to measure the Li abundance in the components of the1 Gyr, [Fe/H]=-0.15 eclipsing short-period binary V505 Per. We find A(Li)=2.7+/-0.1 and 2.4+/-0.2 in the Teff=6500 and 6450 K primary and secondary components, respectively. Previous Teff determinations and uncertainties suggest that each component is located in the midst of the Li dip. If so, their A(Li) are >=2-5 times larger than A(Li) detections and upper limits observed in the similar metallicity and intermediate-age open clusters NGC 752 and 3680, as well as the more metal-rich and younger Hyades and Praesepe. These differences are even larger if the consistent estimates of the scaling ofinitial Li with metallicity inferred from nearby disk stars, open clusters, and recent Galactic chemical evolution models are correct. Our results suggest, independently of complementary evidence based on Li/Be ratios, Be/B ratios, and Li in subgiants evolving out of the Li dip, that main-sequence angular momentum evolution is the origin of the Li dip. Specifically, our stars' A(Li) indicates tidal synchronization can be sufficiently efficient and occur early enough in short-period binary mid-F stars to reduce the effects of rotationally-induced mixing and destruction of Li occuring during the main-sequence in otherwise similar stars that are not short-period tidally-locked binaries.
We discuss concrete examples for frame functions and their associated density operators, as well as for non-Gleason type probability measures.
Microscopic models, which embody the simplicity and significance of a dynamical symmetry approach to nuclear structure, are reviewed. They can reveal striking features of atomic nuclei when a symmetry dominates and solutions in domains that may otherwise be unreachable.
An intriguing phenomenon in topological semimetals and topological insulators is the negative magnetoresistance (MR) observed when a magnetic field is applied along the current direction. A prevailing understanding to the negative MR in topological semimetals is the chiral anomaly, which, however, is not well defined in topological insulators. We calculate the MR of a three-dimensional topological insulator, by using the semiclassical equations of motion, in which the Berry curvature explicitly induces an anomalous velocity and orbital moment. Our theoretical results are in quantitative agreement with the experiments. The negative MR is not sensitive to temperature and increases as the Fermi energy approaches the band edge. The orbital moment and g factors also play important roles in the negative MR. Our results give a reasonable explanation to the negative MR in 3D topological insulators and will be helpful in understanding the anomalous quantum transport in topological states of matter.
From Ref. [Phys. Rev. Lett. 80(1998)4999] one knows that the quantum states secretly chosen from a certain set can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are linearly independent. In this paper, we focus on the probabilistic quantum cloning (PQC) of linearly dependent states with nonnegative cloning efficiencies. We show that a linearly independent subset of the linearly dependent quantum states can be probabilistically cloned if and only if any one state in the subset can not be expressed as the linear superposition of the other states in the set. The optimal possible cloning efficiencies are also investigated.
We consider several families of palintiples (also known as reverse multiples) whose carries themselves are digits of lower-base palintiples and give some methods for constructing them from fundamental palintiple types. We also continue the study of palinomials introduced in an earlier paper by revealing a more direct relationship between the digits of certain palintiple types and the roots of their palinomials. We explore the consequences of this relationship for palinomials induced by palintiple families derived from lower-base palintiples. Finally, we pose some questions regarding Young graphs of derived palintiple families and consider the implications our general observations might have for relations between Young graph isomorphism classes.
Computer vision is a very powerful method for understanding the contents from the images. We tried to utilize this powerful technology to make the difficult task of estimating sheep weights quick and accurate. It has enabled us to minimize the human involvement in measuring weight of the sheep. We are using a novel approach for segmentation and neural network based regression model for achieving better results for the task of estimating sheep weight.
Let $K$ be a number field. The \textit{integral trace form} is the integral quadratic form given by $\text{tr}_{K/\mathbb{Q}}(x^2)|_{O_{K}}.$ In this article we study the existence of non-conjugated number fields with equivalent integral trace forms. As a corollary of one of the main results of this paper, we show that any two non-totally real number fields with the same signature and same prime discriminant have equivalent integral trace forms. Additionally, based on previous results obtained by the author and the evidence presented here, we conjecture that any two totally real quartic fields of fundamental discriminant have equivalent trace zero forms if and only if they are conjugated.
We report results of proper motions of 15 known Large Magellanic Cloud (LMC) old globular clusters (GCs) derived from the Gaia DR2 data sets. When these mean proper motions are gathered with existent radial velocity measurements to compose the GCs' velocity vectors, we found that the projection of the velocity vectors onto the LMC plane and those perpendicular to it tell us about two distinct kinematic GC populations. Such a distinction becomes clear if the GCs are split at a perpendicular velocity of 10 km/s (absolute value). The two different kinematic groups also exhibit different spatial distributions. Those with smaller vertical velocities are part of the LMC disc, while those with larger values are closely distributed like a spherical component. Since GCs in both kinematic-structural components share similar ages and metallicities, we speculate with the possibility that their origins could have occurred through a fast collapse that formed halo and disc concurrently.
$\mathsf{Mn_{3}Sn}$ has recently attracted considerable attention as a magnetic Weyl semimetal exhibiting concomitant transport anomalies at room temperature. The topology of the electronic bands, their relation to the magnetic ground state and their nonzero Berry curvature lie at the heart of the problem. The examination of the full magnetic Hamiltonian reveals otherwise hidden aspects of these unusual physical properties. Here, we report the full spin wave spectra of $\mathsf{Mn_{3}Sn}$ measured over a wide momentum - energy range by the inelastic neutron scattering technique. Using a linear spin wave theory, we determine a suitable magnetic Hamiltonian which not only explains the experimental results but also stabilizes the low-temperature helical phase, consistent with our DFT calculations. The effect of this helical ordering on topological band structures is further examined using a tight-binding method, which confirms the elimination of Weyl points in the helical phase. Our work provides a rare example of the intimate coupling between the electronic and spin degrees of freedom for a magnetic Weyl semimetal system.
We consider some applications of the non-homogeneous second order integral equation of Fox. Some new solutions to Fox's integral equation are discussed in relation to number theory.
The origin of the Nuclear Star Cluster in the centre of our Galaxy is still unknown. One possibility is that it formed after the disruption of stellar clusters that spiralled into the Galactic Centre due to dynamical friction. We trace the formation of the Nuclear Star Cluster around the central black hole, using state-of-the-art N-body simulations, and follow the dynamics of the neutron stars born in the clusters. We then estimate the number of Millisecond Pulsars (MSPs) that are released in the Nuclear Star Cluster, during its formation. The assembly and tidal dismemberment of globular clusters lead to a population of MSPs distributed over a radius of about 20 pc, with a peak near 3 pc. No clustering is found on the sub-parsec scale. We simulate the detectability of this population with future radio telescopes like the MeerKAT radio telescope and SKA1, and find that about of order ten MSPs can be observed over this large volume, with a paucity of MSPs within the central parsec. This helps discriminating this scenario from the in-situ formation model for the Nuclear Star Cluster that would predict an over abundance of MSPs closer to the black hole. We then discuss the potential contribution of our MSP population to the gamma-ray excess at the Galactic Centre.
We present the current status of the research activities of the Ghent group on neutrino-nucleus interactions. These consist in the modeling of some of the relevant neutrino-nucleus reaction channels at intermediate energies: low-energy nuclear excitations, quasielastic scattering, two-nucleon knockout processes and single-pion production.   The low-energy nuclear excitations and the quasielastic peak are described using a Hartree-Fock-CRPA (continuum random phase approximation) model that takes into account nuclear long-range correlations as well as the distortion of the outgoing nucleon wave function. We include two-body current mechanisms through short-range correlations and meson-exchange currents. Their influence on one- and two-nucleon knockout responses is computed. Bound and outgoing nucleons are treated within the same mean-field framework. Finally, for modeling of the neutrino-induced single-pion production, we use a low-energy model that contains resonances and the background contributions required by chiral symmetry. This low-energy model is combined with a Regge approach into a Hybrid model, which allows us to make predictions beyond the resonance region.
We apply the bound on independence number via Lov{\'a}sz theta function to eventown problem and its generalizations over $\mathbb{Z}_n$.
We compare two advanced designs for gravitational-wave antennas in terms of their ability to detect two possible gravitational wave sources. Spherical, resonant mass antennas and interferometers incorporating resonant sideband extraction (RSE) were modeled using experimentally measurable parameters. The signal-to-noise ratio of each detector for a binary neutron star system and a rapidly rotating stellar core were calculated. For a range of plausible parameters we found that the advanced LIGO interferometer incorporating RSE gave higher signal-to-noise ratios than a spherical detector resonant at the same frequency for both sources. Spheres were found to be sensitive to these sources at distances beyond our galaxy. Interferometers were sensitive to these sources at far enough distances that several events per year would be expected.
The effect of density dependent symmetry energy on elliptical flow is studied using isospin-dependent quantum molecular dynamics model(IQMD). We have used the reduced isospin- dependent cross-section with hard(H) equation of state to study the sensitivity of elliptical flow towards symmetry energy in the energy range of 50 - 1000 MeV/nucleon. The elliptical flow becomes zero at a particular energy termed as transition energy. A systematic effort has been made to pin down the transition energy for the density dependent symmetry energy.
It is known that there are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating to the language of $h$-vectors, there are finitely many simplicial complexes of bounded dimension with $h_1=k$ for any natural number $k$. In this paper we study the question at the other end of the $h$-vector: Are there only finitely many $(d-1)$-dimensional simplicial complexes with $h_d=k$ for any given $k$? The answer is no if we consider general complexes, but when focus on three cases coming from matroids: (i) independence complexes, (ii) broken circuit complexes, and (iii) order complexes of geometric lattices. We prove the answer is yes in cases (i) and (iii) and conjecture it is also true in case (ii).
We suggest a way to quantify a type of macroscopic entanglement via distillation of Greenberger-Horne-Zeilinger states by local operations and classical communication. We analyze how this relates to an existing measure of quantum macroscopicity based on the quantum Fisher information in several examples. Both cluster states and Kitaev surface code states are found to not be macroscopically quantum but can be distilled into macroscopic superpositions. We look at these distillation protocols in more detail and ask whether they are robust to perturbations. One key result is that one-dimensional cluster states are not distilled robustly but higher-dimensional cluster states are.
For an isotropic single-band system, it is well known that the semiclassical Boltzmann transport theory within the relaxation time approximation and the Kubo formula with the vertex corrections provide the same result with the $(1-\cos\theta)$ factor in the inverse transport relaxation time. In anisotropic multiband systems, the semiclassical Boltzmann transport equation is generalized to coupled integral equations relating transport relaxation times at different angles in different bands. Using the Kubo formula, we study the vertex corrections to the dc conductivity in anisotropic multiband systems and derive the relation satisfied by the transport relaxation time for both elastic and inelastic scatterings, verifying that the result is consistent with the semiclassical approach.