ShantanuT01/DACTYL-Pretraining huggingface dataset:
We derive an analytical expression for the intermediate scattering function of a particle on a flat surface obeying the Generalised Langevin Equation, with exponential memory friction. Numerical simulations based on an extended phase space method confirm the analytical results. The simulated trajectories provide qualitative insight into the effect that introducing a finite memory timescale has on the analytical line shapes. The relative amplitude of the long-time exponential tail of the line shape is suppressed, but its decay rate is unchanged, reflecting the fact that the cutoff frequency of the exponential kernel affects short-time correlations but not the diffusion coefficient which is defined in terms of a long-time limit. The exponential sensitivity of the relative amplitudes to the decay time of the chosen memory kernel is a very strong indicator for the prospect of inferring a friction kernel and the physical insights from experimentally measured intermediate scattering functions.
High frequency peaked high redshift blazars, are extreme in the sense that their spectrum is particularly hard and peaks at TeV energies. Standard leptonic scenarios require peculiar source parameters and/or a special setup in order to account for these observations. Electromagnetic cascades seeded by ultra-high energy cosmic rays (UHECR) in the intergalactic medium have also been invoked, assuming a very low intergalactic magnetic field (IGMF). Here we study the synchrotron emission of UHECR secondaries produced in blazars located in magnetised environments, and show that it can provide an alternative explanation to these challenged channels, for sources embedded in structured regions with magnetic field strengths of the order of $10^{-7}$ G. To demonstrate this, we focus on three extreme blazars: 1ES 0229+200, RGB J0710+591, and 1ES 1218+304. We model the expected gamma-ray signal from these sources through a combination of numerical Monte Carlo simulations and solving the kinetic equations of the particles in our simulations, and explore the UHECR source and intergalactic medium parameter space to test the robustness of the emission. We show that the generated synchrotron pair halo/echo flux at the peak energy is not sensitive to variations in the overall IGMF strength. This signal is unavoidable in contrast to the inverse Compton pair halo/echo intensity, which is appealing in view of the large uncertainties on the IGMF in voids of large scale structure. It is also shown that the variability of blazar gamma-ray emission can be accommodated by the synchrotron emission of secondary products of UHE neutral beams if these are emitted by UHECR accelerators inside magnetised regions.
In this work I have studied the effect of disorder and system size in fiber bundle model with a certain range of stress redistribution. The strength of the bundle as well as the failure abruptness is observed with varying disorder, stress release range and system sizes. With a local stress concentration, the strength of the bundle is observed to decrease with system size. The behavior of such decrement changes drastically as disorder strength is tuned. At moderate disorder, the critical stress scales with system size in an inverse logarithmic manner. In low disorder, where the brittle response is highly expected, the strength decreases in a scale free manner. With increasing system size and stress release range the model approaches thermodynamic limit and the mean field limit respectively. A detail study expresses different limit in the model and the corresponding modes of failure on the plane of above mentioned parameters.
A complete study of the structure of Ricci collineations for type B warped spacetimes is carried out. This study can be used as a method to obtain these symetries in such spacetimes. Special cases as 2+2 reducible spacetimes, and plane and spherical symmetric spacetimes are considered specifically.
We present the analysis of three kinds of oscillating behavior using multi-wavelength observations of the 10 November 2013 (SOL2013-11-10T05:14) circular-ribbon flare. This event is a typical circular-ribbon flare with an outer spine structure and homologous jets. We found three kinds of oscillations (or perturbations): i) flux oscillation (or QPP) with a dominant period of about 20 seconds in X-ray, EUV, and microwave emissions, ii) periodic jets with an intermittent cadence of around 72 seconds, iii) an outer loop perturbing half a cycle with a duration of about 168 seconds. Similar to the periodic jets that could be produced by a nonthermal process, like repeated magnetic reconnection, the flare QPP detected in the thermal emissions could have the same origin as the oscillation seen in the nonthermal emissions. The outer-loop perturbation is possibly triggered by a blast wave driven by the circular-ribbon flare, or it might be modulated by the sausage wave or the slow magnetoacoustic wave. The results obtained provide data for further numerical studies on the physical origin of the flare oscillations.
In a recent article on stretched polymers in a poor solvent by Grassberger and Hsu \cite{grassberger2002a-a} questions were raised as to the conclusions that can be drawn from currently proposed scaling theory for a single polymer in various types of solution in two and three dimensions. Here we summarise the crossover theory predicted for low dimensions and clarify the scaling arguments that relate thermal exponents for quantities on approaching the $\theta$-point from low temperatures to those associated with the asymptotics in polymer length at the $\theta$-point itself.
The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for m-component reaction-diffusion systems with a tridiagonal symmetric toeplitz matrix of diffusion coefficients and with nonhomogeneous boundary conditions. The proposed technique is based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth.
We study the transverse electron focusing in a two dimensional electron gas with Rashba spin-orbit coupling. We show that the interplay between the external magnetic field and the spin-orbit coupling gives two branches of states with different cyclotron radius within the same energy window. This effect generates a splitting of the first focusing peak in two contributions. Each one of these contributions is spin polarized. The surface reflection mixes the two branches and the second focusing peak does not present the same effect. While for GaAs/AlGaAs heterostructures the effect is small, in systems like InSb/InAlSb the effect should be clearly observed.
Aims - We present the first results of a large spectroscopic survey of globular clusters and candidate globular clusters in the nearby M~31 galaxy. The survey is aimed at the classification of known candidate M~31 clusters and at the study of their kinematic properties. Methods - We obtained low-resolution spectroscopy (lambda/Dlambda~800-1300) for 133 targets, including 76 yet-to-confirm candidate clusters (i.e. with no previous spectroscopic information), 55 already-confirmed genuine M31 clusters, and 2 uncertain candidates. Our observations allowed a reliable estimate of the target radial velocity, within a typical accuracy of ~+-20km/s. The observed candidates have been robustly classified according to their radial velocity and shape parameters that allowed us to confidently discriminate between point sources and extended objects even from low-spatial-resolution imagery. Results - In our set of 76 candidates clusters we found: 42 newly-confirmed bona-fide M~31 clusters, 12 background galaxies, 17 foreground Galactic stars, 2 HII regions belonging to M31 and 3 unclassified (possibly M31 clusters or foreground stars) objects. The classification of a few other candidates not included in our survey has been also reassessed on various observational bases. All the sources of radial velocity estimates for M31 known globular clusters available in the literature have been compared and checked, and a homogeneous general list has been obtained for 349 confirmed clusters with radial velocity. Conclusions - Our results suggest that a significant number of genuine clusters (~> 100) is still hidden among the plethora of known candidates proposed by various authors. Hence our knowledge of the globular cluster system of the M31 galaxy is still far from complete even in terms of simple membership.
Using a symmetrizing operator, we give a new expression for the Omega operator used by MacMahon in Partition Analysis, and given a new life by Andrews and his coworkers. Our result is stated in terms of Schur functions.
Our three-dimensional hydro-dynamical simulations of starbursts examine the formation of superbubbles over a range of driving luminosities and mass loadings that determine superbubble growth and wind velocity. From this we determine the relationship between the velocity of a galactic wind and the power of the starburst. We find a threshold for the formation of a wind, above which the speed of the wind is not affected by grid resolution or the temperature floor of our radiative cooling. We investigate the effect two different temperature floors in our radiative cooling prescription have on wind kinematics and content. We find that cooling to $10$ K instead of to $10^4$ K increases the mass fraction of cold neutral and hot X-ray gas in the galactic wind while halving that in warm H$\alpha$. Our simulations show the mass of cold gas transported into the lower halo does not depend on the starburst strength. Optically bright filaments form at the edge of merging superbubbles, or where a cold dense cloud has been disrupted by the wind. Filaments formed by merging superbubbles will persist and grow to $>400$ pc in length if anchored to a star forming complex. Filaments embedded in the hot galactic wind contain warm and cold gas that moves $300-1200$ km s$^{-1}$ slower than the surrounding wind, with the coldest gas hardly moving with respect to the galaxy. Warm and cold matter in the galactic wind show asymmetric absorption profiles consistent with observations, with a thin tail up to the wind velocity.
We discuss the possibility to modify many-body Hilbert quantum formalism that is necessary for the representation of quantum systems dynamics. The notion of effective classical algorithm and visualization of quantum dynamics play the key role.
In this work, we introduce a novel local pairwise descriptor and then develop a simple, effective iterative method to solve the resulting quadratic assignment through sparsity control for shape correspondence between two approximate isometric surfaces. Our pairwise descriptor is based on the stiffness and mass matrix of finite element approximation of the Laplace-Beltrami differential operator, which is local in space, sparse to represent, and extremely easy to compute while containing global information. It allows us to deal with open surfaces, partial matching, and topological perturbations robustly. To solve the resulting quadratic assignment problem efficiently, the two key ideas of our iterative algorithm are: 1) select pairs with good (approximate) correspondence as anchor points, 2) solve a regularized quadratic assignment problem only in the neighborhood of selected anchor points through sparsity control. These two ingredients can improve and increase the number of anchor points quickly while reducing the computation cost in each quadratic assignment iteration significantly. With enough high-quality anchor points, one may use various pointwise global features with reference to these anchor points to further improve the dense shape correspondence. We use various experiments to show the efficiency, quality, and versatility of our method on large data sets, patches, and point clouds (without global meshes).
Quantum corrections in the hypermultiplet moduli space of type IIA string theories compactified on Calabi-Yau threefolds are investigated.
For a subset $S$ of vertices in a graph $G$, a vertex $v \in S$ is an enclave of $S$ if $v$ and all of its neighbors are in $S$, where a neighbor of $v$ is a vertex adjacent to $v$. A set $S$ is enclaveless if it does not contain any enclaves. The enclaveless number $\Psi(G)$ of $G$ is the maximum cardinality of an enclaveless set in $G$. As first observed in 1997 by Slater [J. Res. Nat. Bur. Standards 82 (1977), 197--202], if $G$ is a graph with $n$ vertices, then $\gamma(G) + \Psi(G) = n$ where $\gamma(G)$ is the well-studied domination number of $G$. In this paper, we continue the study of the competition-enclaveless game introduced in 2001 by Phillips and Slater [Graph Theory Notes N. Y. 41 (2001), 37--41] and defined as follows. Two players take turns in constructing a maximal enclaveless set $S$, where one player, Maximizer, tries to maximize $|S|$ and one player, Minimizer, tries to minimize~$|S|$. The competition-enclaveless game number $\Psi_g^+(G)$ of $G$ is the number of vertices played when Maximizer starts the game and both players play optimally. We study among other problems the conjecture that if $G$ is an isolate-free graph of order $n$, then $\Psi_g^+(G) \ge \frac{1}{2}n$. We prove this conjecture for regular graphs and for claw-free graphs.
We present an analytic model for computing the luminosity and spectral evolution of flares caused by a supermassive black hole impacting the accretion disc of another supermassive black hole. Our model includes photon diffusion, emission from optically thin regions and relativistic corrections to the observed spectrum and time-scales. We test the observability of the impact scenario with a simulated population of quasars hosting supermassive black hole binaries. The results indicate that for a moderate binary mass ratio of 0.3, and impact distances of 100 primary Schwarzschild radii, the accretion disc impacts can be expected to equal or exceed the host quasar in brightness at observed wavelength {\lambda} = 510 nm up to z = 0.6. We conclude that accretion disc impacts may function as an independent probe for supermassive black hole binaries. We release the code used for computing the model light curves to the community.
The coupling parameter series expansion and the high temperature series expansion in the ther- modynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to square-well fluids.
A physical (e.g. astrophysical, geophysical, meteorological etc.) data may appear as an output of an experiment or it may contain some sociological, economic or biological information. Whatever be the source of a time series data some amount of noise is always expected to be embedded in it. Analysis of such data in presence of noise may often fail to give accurate information. Although text book data filtering theory is primarily concerned with the presences of random, zero mean errors; but in reality, errors in data are often systematic rather than random. In the present paper we produce different models of systematic error in the time series data. This will certainly help to trace the systematic error present in the data and consequently that can be removed as possible to make the data compatible for further study.
The quantum approximate optimization algorithm (QAOA) is one of the most prominent proposed applications for near-term quantum computing. Here we study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to optimization problems. We focus on the fundamental boolean satisfiability problem, in the form of random $k$-SAT. We develop analytic bounds on the average success probability of QAOA over random boolean formulae at the satisfiability threshold, as the number of variables $n$ goes to infinity. The bounds hold for fixed parameters and when $k$ is a power of 2. We complement these theoretical results with numerical results on the performance of QAOA for small $n$, showing that these match the limiting theoretical bounds closely. We then use these results to compare QAOA with leading classical solvers. In the case of random 8-SAT, we find that for around 14 ansatz layers, QAOA matches the scaling performance of the highest-performance classical solver we tested, WalkSATlm. For larger numbers of layers, QAOA outperforms WalkSATlm, with an ultimate level of advantage that is still to be determined. Our methods provide a framework for analysing the performance of QAOA for hard constraint satisfaction problems and finding further speedups over classical algorithms.
In this paper we shall survey the various methods of evaluating Hankel determinants and as an illustration we evaluate some Hankel determinants of a q-analogue of Catalan numbers. Here we consider $\frac{(aq;q)_{n}}{(abq^{2};q)_{n}}$ as a q-analogue of Catalan numbers $C_{n}=\frac1{n+1}\binom{2n}{n}$, which is known as the moments of the little q-Jacobi polynomials. We also give several proofs of this q-analogue, in which we use lattice paths, the orthogonal polynomials, or the basic hypergeometric series. We also consider a q-analogue of Schr\"oder Hankel determinants, and give a new proof of Moztkin Hankel determinants using an addition formula for ${}_2F_{1}$.
I discuss the semiclassical approximation for the Wheeler-DeWitt equation when applied to the CGHS model and spherically symmetric gravity. Special attention is devoted to the issues of Hawking radiation, decoherence of semiclassical states, and black hole entropy.
Bekenstein's conjectured entropy bound for a system of linear size $R$ and energy $E$, namely $S \leq 2 \pi E R$, has counterexamples for many of the ways in which the "system," $R$, $E$, and $S$ may be defined. One consistent set of definitions for these quantities in flat Minkowski spacetime is that $S$ is the total von Neumann entropy and $E$ is the expectation value of the energy in a "vacuum-outside-$R$" quantum state that has the the vacuum expectation values for all operators entirely outside a sphere of radius $R$. However, there are counterexamples to the Bekenstein bound for this set of definitions. Nevertheless, an alternative formulation ten years ago by Horacio Casini for the definitions of $S$ and of $2 \pi E R$ have finally enabled a proof for this particular formulation of the Bekenstein bound.
The field dependence of the thermal switching rate of a ferromagnetic material with uniaxial anisotropy was studied by solving the Fokker-Planck equation. We derived the analytical expression of the thermal switching rate using the mean first-passage time approach, and found that Brown's formula [Phys. Rev. 130, 1677 (1963)] is applicable even in the low barrier limit by replacing the attempt frequency with the proper factor which is expressed by the error function.
We show that any hyperplane section of a variety which is the inverse image of a smooth variety of dimension at least 2 by an endomorphism (wich is not an automorphism) of the projective space, is linearly complete. We stress the case of smooth surfaces in projective fourspace.
Let X be a smooth hypersurface in projective space. We discuss in this paper when X can be defined by an equation det M = 0 (resp. pf M = 0), where M is a matrix (resp. a skew-symmetric matrix) with homogeneous entries. Standard homological algebra methods show that this is equivalent to produce a line bundle (resp. a rank 2 vector bundle) E of a certain type on X . We discuss a number of applications for hypersurfaces of small dimension. An Appendix by F.-O. Schreyer proves (using Macaulay 2) that a general form of degree d in P^3 (resp. P^4) can be written as the pfaffian of a skew-symmetric (2d)x(2d) matrix with linear entries in the expected range, that is d < 16 (resp. d < 6).
We consider the problem of rank aggregation based on new distance measures derived through axiomatic approaches and based on score-based methods. In the first scenario, we derive novel distance measures that allow for discriminating between the ranking process of highest and lowest ranked elements in the list. These distance functions represent weighted versions of Kendall's tau measure and may be computed efficiently in polynomial time. Furthermore, we describe how such axiomatic approaches may be extended to the study of score-based aggregation and present the first analysis of distributed vote aggregation over networks.
We show that under some assumptions on the monodromy group some combinations of higher Chern classes of flat vector bundles are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Bloch's conjecture on Chern classes of flat vector bundles on smooth complex projective varities but in some cases they give a more precise information.   We also study Higgs version of Bloch's conjecture and analogous problems in the positive characteristic case.
This paper explores if, and to what an extent, the stellar populations of early type galaxies can be traced through the colour distribution of their globular cluster systems. The analysis, based on a galaxy sample from the Virgo ACS data, is an extension of a previous approach that has been successful in the cases of the giant ellipticals NGC 1399 and NGC 4486, and assumes that the two dominant GC populations form along diffuse stellar populations sharing the cluster chemical abundances and spatial distributions. The results show that a) Integrated galaxy colours can be matched to within the photometric uncertainties and are consistent with a narrow range of ages; b) The inferred mass to luminosity ratios and stellar masses are within the range of values available in the literature; c) Most globular cluster systems occupy a thick plane in the volume space defined by the cluster formation efficiency, total stellar mass and projected surface mass density. The formation efficiency parameter of the red clusters shows a dependency with projected stellar mass density that is absent for the blue globulars. In turn, the brightest galaxies appear clearly detached from that plane as a possible consequence of major past mergers; d) The stellar mass-metallicity relation is relatively shallow but shows a slope change at $M_*\approx 10^{10} M_\odot$. Galaxies with smaller stellar masses show predominantly unimodal globular cluster colour distributions. This result may indicate that less massive galaxies are not able to retain chemically enriched intestellar matter.
The nuclear equation of state and incompressibility are studied in a model with correlations. We first consider a Hartree solution and then add one-particle-one hole (1p-1h) and two particle-two hole (2p-2h) admixtures into the wavefunction using a separable monopole-monopole interaction which induces giant monopole vibrations. Stable and unstable point arise in the nuclear equation of state as a function of the oscillator size parameter from pure 1p-1h admixtures. Addition of 2p-2h admixtures lead to one stable point. However, the incompressibility is found to be quite different from the Hartree case with 1p-1h admixtures, even with 2p-2h states included. PACS 21.65.Mn, 24.30.Cz
Undoped bilayer graphene is a two-dimensional semimetal with a low-energy excitation spectrum that is parabolic in the momentum. As a result, the screening of an arbitrary external charge $Ze$ is accompanied by a reconstruction of the ground state: valence band electrons (for $Z>0$) are promoted to form a space charge around the charge while the holes leave the physical picture. The outcome is flat neutral object resembling the regular atom except that for $Z \gg 1$ it is described by a strictly linear Thomas-Fermi theory. This theory also predicts that the bilayer's static dielectric constant is the same as that of a two-dimensional electron gas in the long-wavelength limit.