ShantanuT01/DACTYL-Pretraining huggingface dataset:
The focus of this work is to create benchmark simulations of decay rates to statistical equilibrium in transport plasma models for Coulomb particle interactions given by a coupled Vlasov-Poisson Fokker-Planck-Landau equation, as well as with Maxwell type and hard sphere interactions. The qualitative decay to the equilibrium Maxwell-Boltzmann distribution through relative entropy is studied in detail for all three types of particle interactions by means of a conservative hybrid spectral and discontinuous Galerkin scheme adapted from previous work. More precisely, the Coulomb case shows that there is a degenerate spectrum, with a decay rate close to the law of two thirds predicted by upper estimates in a work of Strain and Guo in 2006, while the Maxwell type and hard sphere examples both exhibit a spectral gap as predicted by Desvillettes and Villani in 2000. Such decay rate behavior indicates that the analytical estimates for the Coulomb case is sharp while, still to this date, there is no analytical proof of sharp degenerate spectral behaviour for the Fokker-Planck-Landau operator.   Simulations are presented, both for the space-homogeneous case of just particle potential interactions and the space-inhomogeneous case for the mean field coupling through the Poisson equation for total charges in periodic domains. New explicit derivations of spectral collisional weights are presented in the case of Maxwell type and hard sphere interactions and the stability of all three scenarios, including Coulomb interactions, is investigated.
The correct quantum description for a curvature squared term in the action can be obtained by casting the action in the canonical form with the introduction of a variable which is the negative of the first derivative of the field variable appearing in the action, only after removing the total derivative terms from the action. We present the Wheeler-DeWitt equation and obtain the expression for the probability density and current density from the equation of continuity. Furthermore, in the weak energy limit we obtain the classical Einstein equation. Finally we present a solution of the wave equation.
Aims. We investigate the properties of hydrocarbon grains in the galactic superwind of M 82. Methods. With AKARI, we performed near-infrared (2.5 - 4.5 um) spectroscopic observations of 34 regions in M 82 including its northern and southern halos. Results. Many of the spectra show strong emission at 3.3 um due to polycyclic aromatic hydrocarbons (PAHs) and relatively weak features at 3.4 - 3.6 um due to aliphatic hydrocarbons. In particular, we clearly detect the PAH 3.3 um emission and the 3.4 - 3.6 um features in halo regions, which are located at a distance of 2 kpc away from the galactic center. We find that the ratios of the 3.4 - 3.6 um features to the 3.3 um feature intensity significantly increase with distance from the galactic center, while the ratios of the 3.3 um feature to the AKARI 7 um band intensity do not. Conclusions. Our results clearly confirm the presence of small PAHs even in a harsh environment of the halo of M 82. The results also reveal that the aliphatic hydrocarbons emitting the 3.4 - 3.6 um features are unusually abundant in the halo, suggesting that small carbonaceous grains are produced by shattering of larger grains in the galactic superwind.
I present the motivation for studying nuclear collisions at ultrarelativistic energies which is to map the phase diagram of strongly interacting matter under very extreme conditions. The relevant experimental efforts are overviewed and problems in connecting observables with physics of the hot and dense matter are pointed out. I review the current highlights of the experimental programme: excitation functions of various quantities from the SPS which suggest a possibility of the onset of deconfinement, and the evidence of deconfined perfect fluid at RHIC.
This paper considers stochastic population dynamics driven by Levy noise. The contributions of this paper lie in that (a) Using Khasminskii-Mao theorem, we show that the stochastic differential equation associated with the model has a unique global positive solution; (b) Applying an exponential martingale inequality with jumps, we discuss the asymptotic pathwise estimation of such model.
This work sets the exact equations for the quasiclassical response function and susceptibility of a Brownian particle immersed in a bath of quantum harmonic oscillators driving by nonlinear harmonic potentials. A delta force perturbation gives rise to a response whose susceptibility is the combination of a linear term, own of the harmonic oscillator, plus a nonlinear one involving an integral \textcolor{black}{equation. It is provided a recursion method to find its solutions based on functional equations in the Banach space.} The ODE for the response function is a highly nonlinear damped non-autonomous Duffing equation for which the aforementioned method is used to get its solution.
We discuss one of the most prominent features of the very recent preliminary elliptic flow data of $J/\Psi$ meson from the PHENIX collaboration \cite{Silvestre:2008tw}. Even within the the rather large error bars of the measured data a negative elliptic flow parameter ($v_2$) for $J/\Psi$ in the range of $p_T=0.5-2.5 \GeV/c$ is visible. We argue that this negative elliptic flow at intermediate $p_T$ is a clear and qualitative signature for the collectivity of charm quarks produced in nucleus-nucleus reactions at RHIC. Within a parton recombination approach we show that a negative elliptic flow puts a lower limit on the collective transverse velocity of heavy quarks. The numerical value of the transverse flow velocity $\beta_T$ for charm quarks that is necessary to reproduce the data is $\beta_T(charm)\sim 0.55-0.6c$ and therefore compatible with the flow of light quarks.
How to generate provably true randomness with minimal assumptions? This question is important not only for the efficiency and the security of information processing, but also for understanding how extremely unpredictable events are possible in Nature. All current solutions require special structures in the initial source of randomness, or a certain independence relation among two or more sources. Both types of assumptions are impossible to test and difficult to guarantee in practice. Here we show how this fundamental limit can be circumvented by extractors that base security on the validity of physical laws and extract randomness from untrusted quantum devices. In conjunction with the recent work of Miller and Shi (arXiv:1402:0489), our physical randomness extractor uses just a single and general weak source, produces an arbitrarily long and near-uniform output, with a close-to-optimal error, secure against all-powerful quantum adversaries, and tolerating a constant level of implementation imprecision. The source necessarily needs to be unpredictable to the devices, but otherwise can even be known to the adversary.   Our central technical contribution, the Equivalence Lemma, provides a general principle for proving composition security of untrusted-device protocols. It implies that unbounded randomness expansion can be achieved simply by cross-feeding any two expansion protocols. In particular, such an unbounded expansion can be made robust, which is known for the first time. Another significant implication is, it enables the secure randomness generation and key distribution using public randomness, such as that broadcast by NIST's Randomness Beacon. Our protocol also provides a method for refuting local hidden variable theories under a weak assumption on the available randomness for choosing the measurement settings.
We study the possible D-brane configurations in an AdS_3 x S^3 x T^4 background with a NS-NS B field. We use its WZW model description and the boundary state formalism, and we analyze the bosonic and the N=1 supersymmetric cases separately. We also discuss the corresponding classical open string sigma model. We determine the spacetime supersymmetry preserved by the supersymmetric D-brane configurations.
Shadows cast by the rotating black hole in perfect fluid matter are studied using analytical method. We consider three kinds of matter with standard equation of state in Cosmology: $-1/3$ (dark matter), 0 (dust) and $1/3$ (radiation). The apparent shape of the shadow depends on the black hole spin $a$ and the perfect fluid matter intensity $k$. We find that the shadow is a perfect circle in the non-rotating case ($a=0$) and a distorted one in the rotating case ($a\neq0$), similar to what is found for other black holes. Interestingly, different kinds of matter have different influence on the black hole shadow. Dark matter has the strongest effect, dust is the next and radiation is the weakest. By applying our result to the black hole Sgr A$^{*}$ at the center of the Milky Way, we find that the angular resolution required to distinguish among different kinds of matter around the black hole is not much higher than the resolution of current astronomical instruments would be able to achieve in the near future. We propose that observing the black hole shadow provides a possibility of identifying the dominant matter near the black hole.
Certain aspects of the recently proposed antisymmetrised alpha particle product state wave function, or THSR alpha cluster wave function, for the description of the ground state in 8Be, the Hoyle state in 12C, and analogous states in heavier nuclei, are elaborated in detail. For instance, the influence of antisymmetrisation in the Hoyle state on the bosonic character of the alpha particles is studied carefully. It is shown to be weak, so that bosonic aspects are predominant. The de Broglie wave length of alpha particles in the Hoyle state is shown to be much larger than the inter-alpha distance. It is pointed out that the bosonic features of low density alpha gas states have measurable consequences, one of which, that is enhanced multi-alpha decay properties, likely already have been detected. Consistent with experiment, the width of the proposed analogue to the Hoyle state in 16O at the excitation energy of E_x=15.1 MeV is estimated to be very small (34 keV), lending credit to the existence of heavier Hoyle-like states. The intrinsic single boson density matrix of a self-bound Bose system can, under physically desirable boundary conditions, be defined unambiguously. One eigenvalue then separates out, being close to the number of alpha's in the system. Differences between Brink and THSR alpha cluster wave functions are worked out. No cluster model of the Brink type can describe the Hoyle state with a single configuration. On the contrary, many superpositions of the Brink type are necessary, implying delocalisation towards an alpha product state. It is shown that single alpha particle orbits in condensates of different nuclei are almost the same. It is thus argued that alpha particle antisymmetrised product states of the THSR type are a very promising novel and useful concept in nuclear physics.
Recently, many authors showed that if the solar and atmospheric neutrino data are both described by maximal mixing vacuum oscillations at the relevant mass scale, then there exists a unique bi-maximal lepton mixing matrix for three neutrino flavors. We construct the lepton mass matrices from the symmetry principle so that maximal mixings for the atmospheric and the solar neutrino vacuum oscillations are naturally generated. Although the hierarchical patterns of the lepton sector are quite different from each other, we show how two different mass matrices suggested in this work can be generated in a unified way. We also give comments on possible future tests of the bi-maximal lepton mixing matrix.
DUNE (Deep Underground Neutrino Experiment) is a proposed long-baseline neutrino experiment in the US with a baseline of 1300 km from Fermi National Accelerator Laboratory (Fermilab) to Sanford Underground Research Facility, which will house a 40 kt Liquid Argon Time Projection Chamber (LArTPC) as the far detector. The experiment will also have a fine grained near detector for accurately measuring the initial fluxes. We show that the energy range of the fluxes and baseline of the DUNE near detector is conducive for observing $\nu_\mu \to \nu_e$ oscillations of $\Delta m^2 \sim$ eV$^2$ scale sterile neutrinos, and hence can be effectively used for testing to very high accuracy the reported oscillation signal seen by the LSND and MiniBooNE experiments. We study the sensitivity of the DUNE near detector to sterile neutrino oscillations by varying the baseline, detector fiducial mass and systematic uncertainties. We find that the detector mass and baseline of the currently proposed near detector at DUNE will be able to test the entire LSND parameter region with good precision. The dependence of sensitivity on baseline and detector mass is seen to give interesting results, while dependence on systematic uncertainties is seen to be small.
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original ``inertial'' coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein's equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.
Incorporating relational reasoning in neural networks for object recognition remains an open problem. Although many attempts have been made for relational reasoning, they generally only consider a single type of relationship. For example, pixel relations through self-attention (e.g., non-local networks), scale relations through feature fusion (e.g., feature pyramid networks), or object relations through graph convolutions (e.g., reasoning-RCNN). Little attention has been given to more generalized frameworks that can reason across these relationships. In this paper, we propose a hierarchical relational reasoning framework (HR-RCNN) for object detection, which utilizes a novel graph attention module (GAM). This GAM is a concise module that enables reasoning across heterogeneous nodes by operating on the graph edges directly. Leveraging heterogeneous relationships, our HR-RCNN shows great improvement on COCO dataset, for both object detection and instance segmentation.
A long flexible neutral polymer chain immersed in a poor solvent and interacting with an impenetrable attractive surface exhibits a phase known as surface attached globule ({\bf SAG}) in addition to other adsorbed and desorbed phases. In the thermodynamic limit, the {\bf SAG} phase has the same free energy per monomer as the globular phase, and the transition between them is a surface transition. We have investigated the phase diagrams of such a chain in both two- and three- dimensions and calculated the distribution of monomers in different domains of the phase diagram.
Weak lensing of Type Ia supernovae (SNe Ia) is a systematic uncertainty in the use of SNe Ia as standard candles, as well as an independent cosmological probe, if the corresponding magnification distribution can be extracted from data. We study the peak brightness distribution of SNe Ia in the Pantheon sample, and find that the high $z$ sub-sample shows distinct weak lensing signatures compared to the low $z$ subsample: a long tail at the bright end due to high magnifications and a shift of the peak brightness toward the faint end, consistent with findings from earlier work. We have developed a technique to reconstruct the weak lensing magnification distribution of SNe Ia, $p(\mu)$, from the measured SN Ia flux distribution, and applied it to the Pantheon sample. We find that $p(\mu)$ can be reconstructed at a significance better than 2$\sigma$ for the subsample of SNe Ia at $z>0.7$ (124 SNe Ia), and at a lower significance for the SNe Ia at $z>0.9$ (49 SNe Ia), due to the small number of SNe Ia at high redshifts. The large number of $z>1$ SNe Ia from future surveys will enable the use of $p(\mu)$ reconstructed from SNe Ia as an independent cosmological probe.
The NGC 1999 reflection nebula features a dark patch with a size of ~10,000 AU, which has been interpreted as a small, dense foreground globule and possible site of imminent star formation. We present Herschel PACS far-infrared 70 and 160mum maps, which reveal a flux deficit at the location of the globule. We estimate the globule mass needed to produce such an absorption feature to be a few tenths to a few Msun. Inspired by this Herschel observation, we obtained APEX LABOCA and SABOCA submillimeter continuum maps, and Magellan PANIC near-infrared images of the region. We do not detect a submillimer source at the location of the Herschel flux decrement; furthermore our observations place an upper limit on the mass of the globule of ~2.4x10^-2 Msun. Indeed, the submillimeter maps appear to show a flux depression as well. Furthermore, the near-infrared images detect faint background stars that are less affected by extinction inside the dark patch than in its surroundings. We suggest that the dark patch is in fact a hole or cavity in the material producing the NGC 1999 reflection nebula, excavated by protostellar jets from the V 380 Ori multiple system.
We show that the boson field representation of the massless fermion fields, suggested by Morchio, Pierotti and Strocchi in J. Math. Phys. 33, 777 (1992) for the operator solution of the massless Thirring model, agrees completely with the existence of the chirally broken phase in the massless Thirring model revealed in EPJC 20, 723 (2001) and hep-th/0112183, when the free massless boson fields are described by the quantum field theory, free of infrared divergences in 1+1-dimensional space-time, formulated in hep-th/0112184 and hep-th/0204237.
The celebrated Hajnal-Szemer\'edi theorem gives the precise minimum degree threshold that forces a graph to contain a perfect K_k-packing. Fischer's conjecture states that the analogous result holds for all multipartite graphs except for those formed by a single construction. Recently, we deduced an approximate version of this conjecture from new results on perfect matchings in hypergraphs. In this paper, we apply a stability analysis to the extremal cases of this argument, thus showing that the exact conjecture holds for any sufficiently large graph.
The growth in electronic transactions and human machine interactions rely on the information such as gender, age, expression and ethnicity provided by the face image. In order to obtain these information, feature extraction plays a major role. In this paper, retrieval of age, gender, expression and race information from an individual face image is analysed using different feature extraction methods. The performance of four major feature extraction methods such as Active Appearance Model (AAM), Gabor wavelets, Local Binary Pattern (LBP) and Wavelet Decomposition (WD) are analyzed for gender recognition, age estimation, expression recognition and racial recognition in terms of accuracy (recognition rate), time for feature extraction, neural training and time to test an image. Each of this recognition system is compared with four feature extractors on same dataset (training and validation set) to get a better understanding in its performance. Experiments carried out on FG-NET, Cohn-Kanade, PAL face database shows that each method has its own merits and demerits. Hence it is practically impossible to define a method which is best at all circumstances with less computational complexity. Further, a detailed comparison of age estimation and age estimation using gender information is provided along with a solution to overcome aging effect in case of gender recognition. An attempt has been made in obtaining all (i.e. gender, age range, expression and ethnicity) information from a test image in a single go.
We have obtained the correct expression for the centrifugal force acting on a particle at the equatorial circumference of a rotating body in the locally non-rotating frame of the Kerr geometry. Using this expression for the equilibrium of an element on the surface of a slowly rotating Maclaurin spheroid, we obtain the expression for the ellipticity (as discussed earlier by Abramowicz and Miller) and determine the radius at which the ellipticity is maximum.
In this article, we study the one dimensional Heisenberg spin-1/2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and density matrix renormalization groups (DMRG) method, we discuss how the system approaches to the AF uniform spin-1 chain under certain condition. When the ratio of AF to FM coupling strength}$\alpha$ $(\alpha=J_{AF}/J_{F})$ \textit{is very small, the physical quantities of the alternating bond chain such as the spin-spin correlation, the string correlation function and the spin density coincide with that of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with small}$\alpha$\textit{limit. In addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap of the system considered.
The twelve bright (Lx>10(36) erg/s) X-ray sources in the globular clusters have lower luminosities than the brightest sources in the bulge of our galaxy. The dim (Lx<10(35) erg/s) X-ray sources in globular clusters reach higher luminosities than the cataclysmic variables in the disk of our galaxy. The first difference is a statistical fluke, as comparison with M31 indicates. The second difference is explained because the brightest of the dim sources are not cataclysmic variables, but soft X-ray transients in quiescence. This article describes the BeppoSAX, ROSAT and first Chandra observations leading to these conclusions.
The Lagrange theorem on continued fractions states that a number is a quadratic surd if and only if its continued fraction expansion is eventually periodic. The current paper is devoted to a multidimensional generalization of this fact. As a multidimensional analog of continued fractions so called Klein polyhedra are considered: given an irrational lattice in an n-dimensional Euclidean space, its Klein polyhedron is defined as the convex hull of nonzero lattice points with nonnegative coordinates.
Recently we have performed large-scale average magnetization studies of the Ising model for the square, honeycomb, triangular, and simple cubic lattice. We want to complement those studies with the structurally more complicated body-centered cubic lattice Ising model in this paper. We have relevantly calculated the order parameter or average magnetization expression for the body-centered cubic Ising lattice based on the recently developed interrelation, given by $\langle\sigma_{0, i}\rangle= \langle\tanh[K(\sigma_{1,i}+\sigma_{2,i}+\dots +\sigma_{z,i})+H]\rangle$. We will use the same conjectures for the odd spins correlation functions as in our previous works. The mathematical forms of the odd spin correlation functions will be eventually elucidated by some physical discussions. We have seen that the obtained average magnetization expression with the numerical data for the body-centered cubic lattice Ising model is in good agreement.