ShantanuT01/DACTYL-Pretraining huggingface dataset:
We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional $p$-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when $p \ne 2$. We get around this difficulty by working with certain asymptotic estimates for minimizers recently obtained by Brasco, Mosconi and Squassina. The second difficulty is the lack of a direct sum decomposition suitable for applying the classical linking theorem. We use an abstract linking theorem based on the cohomological index proved by Perera and Yang to overcome this difficulty.
A general model for the fragmentation of a two-component system (e.g. protons and neutrons) is proposed and solved exactly. The extension of this model to any number of components is also shown to be exactly solvable. A connection between this models and the permutation group is discussed. The notion of isotopic equivalence is defined in order to evaluate the equivalence of these models to earlier one-component models. All the one-component models considered in earlier papers are shown to be equivalent to a particular class of two-component models. A simplified model applicable to the case of nuclear fragmentation is introduced and analyzed. Modifications to this model to include effects such as pairing and Coulomb interactions are discussed.
The general quasiparticle propagator in dense quark matter is derived for equal mass quarks. Specialized to an NJL model, this propagator includes one new condensate, $\Delta_3$, in addition to the usual CFL condensate, $\Delta_1$. The gap equation is solved in two NJL models and the dependence on the quark mass of the condensates and the gap is presented. Analytic approximations for the condensates are obtained and compared to exact numerical solutions. The results are shown to differ from those obtained by neglecting $\Delta_3$, especially for smaller values of $\Delta_1$. The two different NJL models presented are also shown to give different results when $\Delta_3$ is not neglected. The methods used in this paper can be generalized to the physical case where only the strange quark is significantly massive.
We elaborate the new interpretation of quantum theory that we recently proposed, according to which quantum particles are considered conceptual entities mediating between pieces of ordinary matter which are considered to act as memory structures for them. Our aim is to identify what is the equivalent for the human cognitive realm of what physical space-time is for the realm of quantum particles and ordinary matter. For this purpose, we identify the notion of 'story' as the equivalent within the human cognitive realm of what ordinary matter is in the physical quantum realm, and analyze the role played by the logical connectives of disjunction and conjunction with respect to the notion of locality. Similarly to what we have done in earlier investigations on this new quantum interpretation, we use the specific cognitive environment of the World-Wide Web to elucidate the comparisons we make between the human cognitive realm and the physical quantum realm.
Here we present survey of proper motion stars towards the Galactic Bulge and an adjacent plane region base on VISTA-VVV data. The searching method based on cross-matching photometric Ks-band CASU catalogs. The most interesting discoveries are shown.
We address the issue of massive phase separation (PS) in manganite family of doped Mott insulators through ac conductivity measurements on La$_{0.625-y}$Pr$_{y}$Ca$_{0.375}$MnO$_{3}$ (0.375 $\leq$ y $\leq$ 0.275), and establish applicability of the scaling theory of percolation in the critical regime of the PS. Measurements of dc resistivity, magnetization (M(T)) and electron diffraction show incomplete growth of a ferromagnetic (FM) metallic component on cooling the high temperature charge ordered (CO) phase well below Curie temperature. The impedance $\mid$Z(T,f)$\mid$ measured over a frequency (f) range of 10 Hz to 10 MHz in the critical regime follows a universal scaling of the form $\approx$ R(T,0)g(f$\xi^{2+\theta}$) with $\theta$ $\approx$ 0.86 and the normalized correlation length varying from 1 to 4, suggesting anomalous diffusion of holes in percolating FM clusters.
A novel approach for extracting gauge-invariant information about spin-orbit coupling in gravitationally interacting binary systems is introduced. This approach is based on the "scattering holonomy", i.e. the integration (from the infinite past to the infinite future) of the differential spin evolution along the two worldlines of a binary system in hyperboliclike motion. We apply this approach to the computation, at the first post-Minkowskian approximation (i.e. first order in $G$ and all orders in $v/c$), of the values of the two gyrogravitomagnetic ratios describing spin-orbit coupling in the Effective One-Body formalism. These gyrogravitomagnetic ratios are found to tend to zero in the ultrarelativistic limit.
Hawking effect from the Kinnersley spacetime is investigated using the improved Damour-Ruffini method with a new coordinate transformation. Hawking temperature of the horizons can be obtained point by point. It is found that Hawking temperatures of different points on the horizons are different. Especially, Hawking temperature of Rindler horizon is investigated. The touch between a Kinnersley black hole and its Rindler horizon is considered, and it shows that the phenomenon is related to the third law of thermodynamics.
Dark energy is modelled by a Bose-Einstein gas of particles with an attractive interaction. It is coupled to cold dark matter, within a flat universe, for the late-expansion description, producing variations in particle-number densities. The model's parameters, and physical association, are: $\Omega_{G0}$, $\Omega_{m0}$, the dark-energy rest-mass energy density and the dark-matter term scaling as a mass term, respectively; $\Omega_{i0}$, the self-interaction intensity; $x$, the energy exchange rate. Energy conservation relates such parameters. The Hubble equation omits $\Omega_{G0}$, but also contains $h$, the present-day expansion rate of the flat Friedman--Lem\^aitre--Robertson--Walker metric, and $\Omega_{b0}$, the baryon energy density, used as a prior. This results in the four effective chosen parameters $\Omega_{b0}$, $h$, $\Omega_{m0}$, $\Omega_{i0}$, fit with the Hubble expansion rate $H(z)$, and data from its value today, near distance, and supernovas. We derive wide $1\sigma$ and $2\sigma$ likelihood regions compatible with definite positive total CDM and IBEG mass terms. Additionally, the best-fit value of parameter $x$ relieves the coincidence problem, and a second potential coincidence problem related to the choice of $\Omega_{G0}$.
With new data sets, recently completed analyses and renewed interest, there has been significant progress in addressing existing questions about quarkonia production and decay ... but also new questions and new confrontation with theory. Some highlights include the firm establishment of the eta_c^' and of the ``missing'' psi^' decays to pseudoscalar-vector final states, improved information on the nature of the psi(3770), and the observation of a new, puzzling charmonium-like state at 3872 MeV.
We study the sensitivity limits of a broadband gravitational-waves detector based on dual resonators such as nested spheres. We determine both the thermal and back-action noises when the resonators displacements are read-out with an optomechanical sensor. We analyze the contributions of all mechanical modes, using a new method to deal with the force-displacement transfer functions in the intermediate frequency domain between the two gravitational-waves sensitive modes associated with each resonator. This method gives an accurate estimate of the mechanical response, together with an evaluation of the estimate error. We show that very high sensitivities can be reached on a wide frequency band for realistic parameters in the case of a dual-sphere detector.
This paper has been withdrawn by the author due to a necessity of further editing. (Will be resubmitted here or elsewhere in editted form.)
An InfoCGAN neural network is trained on 2-dimensional square Ising configurations conditioned on the external applied magnetic field and the temperature. The network is composed of two main sub-networks. The generator network learns to generate convincing Ising configurations and the discriminator network learns to discriminate between "real" and "fake" configurations with an additional categorical assignment prediction provided by an auxiliary network. Some of the predicted categorical assignments show agreement with the expected physical phases in the Ising model, the ferromagnetic spin-up and spin down phases as well as the high temperature weak external field phase. Additionally, configurations associated with the crossover phenomena are predicted by the model. The classification probabilities allow for a robust method of estimating the critical temperature in the vanishing field case, showing exceptional agreement with the known physics. This work indicates that a representation learning approach using an adversarial neural network can be used to identify categories that strongly resemble physical phases with no a priori information beyond raw physical configurations and the physical conditions they are subject to.
We investigate a string model defined by a special plane-wave metric ds^2 = 2dudv - l(u) x^2 du^2 + dx^2 with l(u) = k/u^2 and k=const > 0. This metric is a Penrose limit of some cosmological, Dp-brane and fundamental string backgrounds. Remarkably, in Rosen coordinates the metric has a ``null cosmology'' interpretation with flat spatial sections and scale factor which is a power of the light-cone time u. We show that: (i) This spacetime is a Lorentzian homogeneous space. In particular, like Minkowski space, it admits a boost isometry in u,v. (ii) It is an exact solution of string theory when supplemented by a u-dependent dilaton such that its exponent (i.e. effective string coupling) goes to zero at u=infinity and at the singularity u=0, reducing back-reaction effects. (iii) The classical string equations in this background become linear in the light-cone gauge and can be solved explicitly in terms of Bessel's functions; thus the string model can be directly quantized. This allows one to address the issue of singularity at the string-theory level. We examine the propagation of first-quantized point-particle and string modes in this time-dependent background. Using certain analytic continuation prescription we argue that string propagation through the singularity can be smooth.
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not depend on local anisotropies. These two quantities have the same value as in the standard percolation in regular bidimensional lattices. On the other side, the scaling of the correlation length ($\nu$ exponent) unfolds new universality classes due to the local anisotropy of the critical percolation cluster. We use two critical exponents $\nu$ according to the percolation criterion for crossing the lattice in either direction or in both directions. Moreover $\nu$ is related to a parameter that characterizes the stretching of the blocks forming the tilling of the multifractal.
We present the color distributions of globular cluster (GC) systems for 100 Virgo cluster early-type galaxies observed in the ACS Virgo Cluster Survey. The color distributions of individual GC systems are consistent with continuous trends across galaxy luminosity, color, and stellar mass. On average, almost all galaxies possess a component of metal-poor GCs, with the average fraction of metal-rich GCs ranging from 15 to 60%. The colors of both subpopulations correlate with host galaxy luminosity and color, with the red GCs having a steeper slope. To convert color to metallicity, we also introduce a preliminary (g-z)-[Fe/H] relation calibrated to Galactic, M49 and M87 GCs. This relation is nonlinear with a steeper slope for [Fe/H] < -0.8. As a result, the metallicities of the metal-poor and metal-rich GCs vary similarly with respect to galaxy luminosity and stellar mass, with relations of [Fe/H]_MP ~ L^0.16 ~ M_star^0.17 and [Fe/H]_MR ~ L^0.26 ~ M_star^0.22, respectively. Although these relations are shallower than the mass-metallicity relation predicted by wind models and observed for dwarf galaxies, they are very similar to the mass-metallicity relation for star forming galaxies in the same mass range. The offset between the two GC populations varies slowly (~ M_star^0.05) and is approximately 1 dex across three orders of magnitude in mass, suggesting a nearly universal amount of enrichment between the formation of the two populations of GCs. We also find that although the metal-rich GCs show a larger dispersion in color, it is the *metal-poor GCs* that have an equal or larger dispersion in metallicity. Like the color-magnitude relation, these relations derived from globular clusters present stringent constraints on the formation and evolution of early-type galaxies. (Abridged)
Core overshoot is a large source of uncertainty in constructing stellar models. Whether the amount of overshoot is constant or mass dependent is not completely known, even though models sometimes assume a mass-based trend. In this work we use asteroseismic data from stars observed by \textit{Kepler} to investigate the relationship between various stellar properties and the amount of overshoot needed to properly model a given star. We find a strong positive trend between stellar mass and overshoot amount for stars between 1.1 and 1.5 $M_\odot$, with a slope of 0.89. Additionally, we investigate how inferred stellar properties change as a function of overshoot. Our model grids show that the inferred stellar mass and radius can vary by as much as 14\% and 6\% respectively, depending on the extent of overshoot. This mass spread results in a commensurate spread in the ages.
A general framework for a systematic quasi-localization of canonical general relativity and a new ingredient, the requirement of the gauge invariance of the boundary terms appearing in the calculation of Poisson brackets, are given. As a consequence of this it is shown, in particular, that the generator vector fields (built from the lapse and shift) of the quasi-local quantities must be divergence free with respect to a Sen-type connection; and the volume form induced from the spatial metric on the boundary surface must be fixed.
Zeros of entire functions can be found using either the Fourier methods of Riemann-Polya or the Generalized Gamma Convolution (GGC) methods of Thorin-Bondesson. This connection is based on a duality between the Hadamard-Weierstrass factorisation and van Dantzig Pairs-Wald couples of random variables. We demonstrate the methodology on particular functions including the Riemann zeta and xi-functions, Ramanujan's tau function, L-functions and Gamma and Hyperbolic functions.
We present a novel source for supersymmetry breaking in orientifold models, and show that it gives a vanishing contribution to the vacuum energy at genus zero and three-half. We also argue that all the corresponding perturbative contributions to the vacuum energy from higher-genus Riemann surfaces vanish identically.
Background boucing cosmologies in the framework of General Relativity, driven by a single scalar field filling the Universe, and with a quasi-matter domination period, i.e., depicting the so-called Matter Bounce Scenario, are reconstructed for geometries with positive spatial curvature. These cosmologies lead to a nearly flat power spectrum of the curvature fluctuations in co-moving coordinates for modes that leave the Hubble radius during the quasi-matter domination period, and whose spectral index and its running, which are related with the effective Equation of State parameter given by the quotient of the pressure over the energy density, are compatible with observational data.
The calculation of the stress field around an arbitrarily shaped crack in an infinite two-dimensional elastic medium is a mathematically daunting problem. With the exception of few exactly soluble crack shapes the available results are based on either perturbative approaches or on combinations of analytic and numerical techniques. We present here a general solution of this problem for any arbitrary crack. Along the way we develop a method to compute the conformal map from the exterior of a circle to the exterior of a line of arbitrary shape, offering it as a superior alternative to the classical Schwartz-Cristoffel transformation. Our calculation results in an accurate estimate of the full stress field and in particular of the stress intensity factors K_I and K_{II} and the T-stress which are essential in the theory of fracture.
We generalize Givental's Theorem for complete intersections in smooth toric varieties in the Fano case. In particular, we find Gromov--Witten invariants of Fano varieties of dimension $\geq 3$, which are complete intersections in weighted projective spaces and singular toric varieties. We generalize the Riemann-Roch equations to weighted projective spaces. We compute counting matrices of smooth Fano threefolds with Picard group Z and anticanonical degrees 2, 8, and 16.
We examined the relations between molecular gas surface density and star formation rate surface density in a 11 square degree region of the Galactic Plane. Dust continuum at 1.1 mm from the Bolocam Galactic Plane Survey and 22 micron emission from the WISE All-sky survey were used as tracers of molecular gas and star formation rate, respectively, across Galactic longitude of 31.5 > l > 20.5 and Galactic latitude of 0.5 > b > -0.5. The relation was studied over a range of resolutions from 33 arcsecond to 20 arcminute by convolving images to larger scales. The pixel-by-pixel correlation between 1.1 mm and 22 micron increases rapidly at small scales and levels off at the scale of 5 - 8 arcminute. We studied the star formation relation based on pixel-by-pixel analysis and 1.1 mm and 22 micron peaks analysis. The star formation relation was found to be nearly linear with no significant changes in the form of the relation across all spatial scales and lie above the extragalactic relation from Kennicutt (1998). The average gas depletion time is approximately 200 Myr and does not change significantly at different scales, but the scatter in the depletion time decreases as the scale increases.
In this letter we calculate the energy loss of highly magnetized neutron star due to friction with quantum vacuum, namely Quantum Vacuum Friction (QVF). Taking into account one-loop corrections in the effective Heisenberg-Euler Lagrangian of the light-light interaction, we derive an analytic expression for QVF allowing us to consider magnetic field at the surface of the star as high as $10^{11} $T. In the case of magnetars with high magnetic field above the QED critical field, we show that the energy loss by QVF dominates the energy loss process. This has important consequences, in particular on the inferred value of the magnetic field. This also indicates the need for independent measurements of magnetic field, energy loss rate, and of the braking index to fully characterize magnetars.
The structure and spectrum of the accretion shock have been self-consistently simulated for a wide range of parameters typical for Classical T Tauri Stars (CTTS). Radiative cooling of the shocked gas was calculated, taking into account the self-absorption and non-equilibrium (time-dependent) effects in the level populations. These effects modify the standard cooling curve for an optically thin plasma in coronal equilibrium, however the shape of high-temperature ($T>3\times10^5$ K) part of the curve remains unchanged. The applied methods allow us to smoothly describe the transition from the cooling flow to the hydrostatic stellar atmosphere. Thanks to this approach, it has been found that the narrow component of HeII lines is formed predominantly in the irradiated stationary atmosphere (hotspot), i.e. at velocities of the settling gas $<2$ km s$^{-1}$. The structure of the pre-shock region is calculated simultaneously with the heated atmosphere. The simulation shows that the pre-shock gas produces a noticeable emission component in HeII lines and practically does not manifest itself in HeI lines ($\lambda\lambda$ 5876, 10830 {\AA}). The UV spectrum of the hotspot is distorted by the pre-shock gas, namely numerous red-shifted emission and absorption lines overlap each other forming a pseudo-continuum. The spectrum of the accretion region at high pre-shock densities $\sim10^{14}$ cm$^{-3}$ is fully formed in the in-falling gas and can be qualitatively described as a spectrum of a star with an effective temperature derived from the Stefan-Boltzmann law via the full energy flux.
We study a queueing system with Erlang arrivals with $k$ phases and Erlang service with $m$ phases. Transition rates among phases vary periodically with time. For these systems, we derive the asymptotic periodic distribution of the level and phase as a function of time within the period. The asymptotic periodic distribution is analogous to a steady-state distribution for a system with constant rates. If the time within the period is considered part of the state, then it is a steady-state distribution. We also obtain waiting time and busy period distributions. These solutions are expressed as infinite series. We provide bounds for the error of the estimate obtained by truncating the series. Examples are provided comparing the solution of the system of ordinary differential equation with a truncated state space to these asymptotic solutions involving remarkably few terms of the infinite series.
Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators. As the natural counterpart of the popular maximum-likelihood point estimator, we introduce the maximum-likelihood region---the region of largest likelihood among all regions of the same size. Here, the size of a region is its prior probability. Another concept is the smallest credible region---the smallest region with pre-chosen posterior probability. For both optimization problems, the optimal region has constant likelihood on its boundary. We discuss criteria for assigning prior probabilities to regions, and illustrate the concepts and methods with several examples.
In this paper, by introducing a new operation in the vector space of analytic functions, the author presents a method for derivating the well-known formulas: $\zeta(1-k)=-\frac{B_k}{k}$ and $\zeta(1-n,a)=-\frac{B_n(a)}{n}$ , where $\zeta$, $\zeta(1-n,a)$ denote the Riemann zeta function and the Hurwitz zeta function respectively. $B_k$ is the $k$-th Bernoulli number. Also the author steps further to deduce some identities related to Bernoulli number and Bernoulli polynomial. Moreover, when combining the operation with forward difference, we can show a new formula for Riemann zeta function, i.e. \[\zeta(s)=e\sum_{n=0}^{\infty}\sum_{i=0}^{n}(-1)^{n-i}\frac{1}{(n-i)!(1+i)^{s}}.\]
The measurement of gamma rays from the diffuse afterglow of radioactivity originating in massive-star nucleosynthesis is considered a laboratory for testing models, when specific stellar groups are investigated, at known distance and with well-constrained stellar population. Regions which have been exploited for such studies include Cygnus, Carina, Orion, and Scorpius-Centaurus. The Orion region hosts the Orion OB1 association and its subgroups at about 450~pc distance. We report the detection of $^{26}$Al gamma rays from this region with INTEGRAL/SPI.