ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we show that the eigenvalues of certain classes of Cayley graphs are integers. The (n,k,r)-arrangement graph A(n,k,r) is a graph with all the k-permutations of an n-element set as vertices where two k-permutations are adjacent if they differ in exactly r positions. We establish a relation between the eigenvalues of the arrangement graphs and the eigenvalues of certain Cayley graphs. As a result, the conjecture on integrality of eigenvalues of A(n,k,1) follows.
Phenomenological effective interactions like Skyrme forces are currently used in mean--field calculations in nuclear physics. Mean--field models have strong analogies with the first order of the perturbative many--body problem and the currently used effective interactions are adjusted at the mean--field level. In this work, we analyze the renormalizability of the nuclear many--body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.
We study the Brill-Noether stratification of the coarse moduli space of locally free stable and flat sheaves of a compact Kahler manifold, proving that these strata have quadratic algebraic singularities.
We correct a mistake in \cite{St} leading to erroneous formulas in Theorems 5.2 and 5.4. As an immediate corollary of a formula in \cite{BCJ} we give a formula, which relates the Hecke operators $T(p^2)\circ T(p^{2l-2})$, $T(p^{2l})$ and $T(p^{2l-4})$ and comment on it.
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
A combined interpretation of the CALET $e^+\, +\, e^-$ spectrum up to 3 TeV and the AMS-02 positron spectrum up to 500 GeV was performed and the results are discussed. To parametrize the background electron flux, we assume a smoothly broken power-law spectrum with an exponential cut-off for electrons and fit this parametrization to the measurements, with either a pulsar or 3-body decay of fermionic Dark Matter as the extra electron-positron pair source responsible for the positron excess. We found that depending on the parameters for the background, both Dark Matter decay and the pulsar model can explain the combined measurements. While the Dark Matter decay scenario is constrained by the Fermi-LAT $\gamma$-ray measurement, we show that 3-body decay of a 800 GeV Dark Matter can be compatible with the $\gamma$-ray flux measurement. We discuss the capability of CALET to discern decaying Dark Matter models from a generic pulsar source scenario, based on simulated data for five years of data-taking.
Accretion-induced collapse (AIC) occurs when an O/Ne white dwarf (WD) grows to nearly the Chandrasekhar mass ($M_{\rm Ch}$), reaching central densities that trigger electron captures in the core. Using Modules for Experiments in Stellar Astrophysics ($\texttt{MESA}$), we present the first true binary simulations of He star + O/Ne WD binaries, focusing on a $1.5 M_\odot$ He star in a 3 hour orbital period with $1.1-1.3 M_\odot$ O/Ne WDs. The helium star fills its Roche lobe after core helium burning is completed and donates helium on its thermal timescale to the WD, $\dot{M}\approx3\times10^{-6} M_\odot$/yr, a rate high enough that the accreting helium burns stably on the WD. The accumulated carbon/oxygen ashes from the helium burning undergo an unstable shell flash that initiates an inwardly moving carbon burning flame. This flame is only quenched when it runs out of carbon at the surface of the original O/Ne core. Subsequent accumulation of fresh carbon/oxygen layers also undergo thermal instabilities, but no mass loss is triggered, allowing $M_{\rm WD}\rightarrow M_{\rm Ch}$, triggering the onset of AIC. We also discuss the scenario of accreting C/O WDs that experience shell carbon ignitions to become O/Ne WDs, and then, under continuing mass transfer, lead to AIC. Studies of the AIC event rate using binary population synthesis should include all of these channels, especially this latter channel, which has been previously neglected but might dominate the rate.
Some short gamma-ray bursts (SGRBs) are thought to be caused by the mergers of binary neutron stars which may sometimes produce massive neutron star remnants capable of producing extragalactic fast radio bursts (FRBs). We conducted a deep search for FRBs from the sites of six low-redshift SGRBs. We collected high time- and frequency-resolution data from each of the sites for 10 hours using the 2 GHz receiver of the Green Bank Telescope. Two of the SGRB sites we targeted were visible with the Arecibo Radio Telescope with which we conducted an additional 10 hours of 1.4 GHz observations for each. We searched our data for FRBs using the GPU-optimized dedispersion algorithm $\texttt{heimdall}$ and the machine-learning-based package $\texttt{FETCH}$ (Fast Extragalactic Transient Candidate Hunter). We did not discover any FRBs, but would have detected any with peak flux densities in excess of 87 mJy at the Green Bank Telescope or 21 mJy at Arecibo with a signal-to-noise ratio of at least 10. The isotropic-equivalent energy of any FRBs emitted from these sites in our bands during our observations must not have exceeded a few times $10^{38}$ erg, comparable to some of the lowest energy bursts yet seen from the first known repeating FRB 121102.
Shifting the Fermi energy in solids by doping, defect formation or gating generally results in changes in the charge density distribution, which reflect the ability of the bonding pattern in solids to adjust to such external perturbations. In the ionic limit, such changes are described by the formal oxidation states (FOS) whereby a single atom type is presumed to absorb the full burden of the perturbation (change in charge) of the whole compound. In this picture, when the solar absorber CsSnI3 loses 50 % of its Sn atoms thereby forming the ordered vacancy compound Cs2SnI6, the Sn is said to change from Sn2+ to Sn4+. In reality, the charge redistribution is more complex. To understand the electronic properties of these two groups and to gauge the trends in s-electron charge on the nucleus, we studied the 113/216 compound pairs CsSnCl3/Cs2SnCl6; CsSnBr3/Cs2SnBr6, and CsSnI3/Cs2SnI6. We have calculated the electronic structure of these three compound pairs, complementing them by CsSnF3/Cs2SnF6 in the hypothetical cubic structure for completing the chemical trends. These materials were also synthesized by chemical routes and characterized by X-ray diffraction, Mossbauer spectroscopy and K-edge X-ray Absorption Spectroscopy. We find that in going from 113 to 216 there is a decrease in the s charge on Sn, in agreement with the FOS picture. However, at the same time, we observe an increase of the p charge via downshift of the otherwise unoccupied p level, an effect that tends to replenish much of the lost s charge. This effect is theoretically explained as a self-regulating response [H. Raebiger, S. Lany, and A. Zunger, Nature 453, 763 (2008)] whereby the system re-hybridizes to minimize the effect of the charge perturbation created by vacancy formation. Our work clarifies the relation between FOS and charge transfer that can be applied to a wide variety of materials.
Strange and charmed baryon productions from proton-antiproton collisions are studied in the effective Lagrangian and Regge approaches. We include only the $t$-channel dynamics which is dominant for the diffractive region that is relevant in the present discussions. For strangeness productions, the coupling constants for $K$ meson are determined by $SU(3)$ relations while other unknown parameters for $K^{*}$ couplings and for form factors are fixed by existing observed data for strangeness productions. By extrapolating the amplitudes for strangeness productions to those for charm, we predict charm production cross sections. It turns out that the total cross sections are $10^{4}$ to $10^{5}$ smaller than those of strangeness productions, depending on the final states. By using the known total cross sections for strangeness, $\sim 10^{2} \mu b$ for $\Lambda \bar{\Lambda}$ and, $\sim 10^{1} \mu b$ for $\Sigma \bar{\Lambda}$ the total cross sections for charm productions are predicted to be $\sim 10^{-2} \mu b$ for $\Lambda_{c} \bar{\Lambda}_c$, $\sim 10^{-3} \mu b$ for $\Sigma_{c} \bar{\Lambda}_c$, and $\sim 10^{-4} \mu b$ for $\Sigma_{c} \bar{\Sigma}_c$. Our results can be tested in the future experiments at $\bar{\text{P}}$ANDA.
The influence of considering a generalized dark matter (GDM) model, which allows for a non-pressure-less dark matter and a non-vanishing sound speed in the non-linear spherical collapse model is discussed for the Einstein-de Sitter-like (EdSGDM) and $\Lambda$GDM models. By assuming that the vacuum component responsible for the accelerated expansion of the Universe is not clustering and therefore behaving similarly to the cosmological constant $\Lambda$, we show how the change in the GDM characteristic parameters affects the linear density threshold for collapse of the non-relativistic component ($\delta_{\rm c}$) and its virial overdensity ($\Delta_{\rm V}$). We found that the generalized dark matter equation of state parameter $w_{\rm gdm}$ is responsible for lower values of the linear overdensity parameter as compared to the standard spherical collapse model and that this effect is much stronger than the one induced by a change in the generalized dark matter sound speed $c^2_{\rm s, gdm}$. We also found that the virial overdensity is only slightly affected and mostly sensitive to the generalized dark matter equation of state parameter $w_{\rm gdm}$. These effects could be relatively enhanced for lower values of the matter density. Finally, we found that the effects of the additional physics on $\delta_{\rm c}$ and $\Delta_{\rm V}$, when translated to non-linear observables such as the halo mass function, induce an overall deviation of about 40\% with respect to the standard $\Lambda$CDM model at late times for high mass objects. However, within the current linear constraints for $c^2_{\rm s, gdm}$ and $w_{\rm gdm}$, we found that these changes are the consequence of properly taking into account the correct linear matter power spectrum for the GDM model while the effects coming from modifications in the spherical collapse model remain negligible.
Primordial magnetic fields lead to non-Gaussian signals in the Cosmic Microwave Background (CMB) even at the lowest order, as magnetic stresses, and the temperature anisotropy they induce, depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arise only as a higher order effect. We propose here a novel probe of stochastic primordial magnetic fields that exploits the characteristic CMB non-Gaussianity that they induce. In particular, we compute the CMB bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by stochastic primordial fields on large angular scales. We find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \sim 10^{-22}$, for magnetic fields of strength $B_0 \sim 3$ nano Gauss and with a nearly scale invariant magnetic spectrum. Current observational limits on the bispectrum allow us to set upper limits on $B_0 \sim 35$ nano Gauss, which can be improved by including other magnetically induced contributions to the bispectrum.
We present a timing analysis of the 2015 outburst of the accreting millisecond X-ray pulsar SAX J1808.4-3658, using non-simultaneous XMM-Newton and NuStar observations. We estimate the pulsar spin frequency and update the system orbital solution. Combining the average spin frequency from the previous observed, we confirm the long-term spin down at an average rate $\dot{\nu}_{\text{SD}}=1.5(2)\times 10^{-15}$ Hz s$^{-1}$. We also discuss possible corrections to the spin down rate accounting for mass accretion onto the compact object when the system is X-ray active. Finally, combining the updated ephemerides with those of the previous outbursts, we find a long-term orbital evolution compatible with a binary expansion at a mean rate $\dot{P}_{orb}=3.6(4)\times 10^{-12}$ s s$^{-1}$, in agreement with previously reported values. This fast evolution is incompatible with an evolution driven by angular momentum losses caused by gravitational radiation under the hypothesis of conservative mass transfer. We discuss the observed orbital expansion in terms of non-conservative mass transfer and gravitational quadrupole coupling mechanism. We find that the latter can explain, under certain conditions, small fluctuations (of the order of few seconds) of the orbital period around a global parabolic trend. At the same time, a non-conservative mass transfer is required to explain the observed fast orbital evolution, which likely reflects ejection of a large fraction of mass from the inner Lagrangian point caused by the irradiation of the donor by the magneto-dipole rotator during quiescence (radio-ejection model). This strong outflow may power tidal dissipation in the companion star and be responsible of the gravitational quadrupole change oscillations.
Let $(X,\Delta)$ be a 4-dimensional log variety which is proper over the field of complex numbers and with only divisorial log terminal singularities. The log canonical divisor $K_X+\Delta$ is semi-ample, if it is nef (numerically effective) and the Iitaka dimension $\kappa(X,K_X+\Delta)$ is strictly positive. For the proof, we use Fujino's abundance theorem for semi log canonical threefolds.
The discovery of acceleration and dark energy arguably constitutes the most revolutionary discovery in astrophysics in recent years. Cerro Tololo Inter-American Observatory (CTIO) played a key role in this amazing discovery through three systematic supernova surveys organized by staff astronomers: the "Tololo Supernova Program" (1986-2000), the Calan/Tololo Project (1989-1993), and the "High-Z Supernova Search Team" (1994-1998). CTIO's state of the art instruments also were fundamental in the independent discovery of acceleration by the "Supernova Cosmology Project" (1992-1999). Here I summarize the work on supernovae carried out from CTIO that led to the discovery of acceleration and dark energy and provide a brief historical summary on the use of Type Ia supernovae in cosmology in order to provide context for the CTIO contribution.
Magnetization dynamics described by the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation can be formulated to have the form of the well-known two-level-system (TLS) equations. Recently, we showed that a DC spin-transfer torque (STT) term in the LLGS equation can be mapped to a modulation of the carrier relaxation rates in the analogous TLS equations. Here, we extend the analogy to the TLS dynamics by including the AC magnetic field, AC demagnetization field, and AC STT excitation that we show constitute the interaction term in the analogous TLS picture. Interestingly, we find that the carrier injection rate in the TLS equations that is responsible for transitions between the excited and ground states of the system naturally translates to an intense short magnetic pulse that reverses the magnetization state. Furthermore, we also show that the two helicities of circularly polarized magnetic pulses correspond to the two carrier injection rates in the analogous TLS picture. In the context of the highly debated all-optical helicity dependent switching experiment, it offers a new explanation of the magnetization reversal from first principles.
The two-channel Anderson impurity model serves as a prototype for describing heavy-fermion materials with a possible mixed-valent regime with both quadrupolar and magnetic character. We report on the low-energy physics of the model, using a conformal field theory approach with exact Bethe Ansatz results as input.
We discuss the nonmesonic decay of deformed p-shell hypernuclei. The Nilsson model with angular momentum projection is employed in order to take into account the deformation effects. The nonmesonic decay rate and the intrinsic $\Lambda$ asymmetry parameter decrease as a function of the deformation parameter, while the ratio of the neutron- to proton-induced decay rates increases. We find that the deformation effects change these observables by about 10 % for $^9_{\Lambda}$Be from the spherical limit.
In this paper we propose a scheme which allows one to find all possible exponential solutions of special class -- non-constant volume solutions -- in Lovelock gravity in arbitrary number of dimensions and with arbitrate combinations of Lovelock terms. We apply this scheme to (6+1)- and (7+1)-dimensional flat anisotropic cosmologies in Einstein-Gauss-Bonnet and third-order Lovelock gravity to demonstrate how our scheme does work. In course of this demonstration we derive all possible solutions in (6+1) and (7+1) dimensions and compare solutions and their abundance between cases with different Lovelock terms present. As a special but more "physical" case we consider spaces which allow three-dimensional isotropic subspace for they could be viewed as examples of compactification schemes. Our results suggest that the same solution with three-dimensional isotropic subspace is more "probable" to occur in the model with most possible Lovelock terms taken into account, which could be used as kind of anthropic argument for consideration of Lovelock and other higher-order gravity models in multidimensional cosmologies.
The inferred black hole in the Galactic center spans the largest angle on the sky among all known black holes. Forthcoming observational programs plan to localize or potentially resolve the image of Sgr A* to an exquisite precision, comparable to the scale of the black hole horizon. Here we show that the location of the image centroid of Sgr A* should depend on observing frequency because of relativistic and radiative transfer effects. The same effects introduce a generic dependence of the source polarization on frequency. Future detection of the predicted centroid shift and the polarization dependence on frequency can be used to determine the unknown black hole spin and verify the validity of General Relativity.
Using a three-dimensional magnetohydrodynamic model, we simulate the magnetic reconnection in a single current sheet. We assume a finite guide field, a random perturbation on the velocity field and uniform resistivity. Our model enhances the reconnection rate relative to the classical Sweet-Parker model in the same configuration. The efficiency of magnetic energy conversion is increased by interactions between the multiple tearing layers coexisting in the global current sheet. This interaction, which forms a positive-feedback system, arises from coupling of the inflow and outflow regions in different layers across the current sheet. The coupling accelerates the elementary reconnection events, thereby enhancing the global reconnection rate. The reconnection establishes flux tubes along each tearing layer. Slow-mode shocks gradually form along the outer boundaries of these tubes, further accelerating the magnetic energy conversion.Such positive-feedback system is absent in two-dimensional simulation, three-dimensional reconnection without a guide field and a reconnection under a single perturbation mode. We refer to our model as the "shock-evoking positive-feedback" model.
We consider the nonlinear Schr\"{o}dinger equation on the half-line $x \geq 0$ with a Robin boundary condition at $x = 0$ and with initial data in the weighted Sobolev space $H^{1,1}(\mathbb{R}_+)$. We prove that there exists a global weak solution of this initial-boundary value problem and provide a representation for the solution in terms of the solution of a Riemann--Hilbert problem. Using this representation, we obtain asymptotic formulas for the long-time behavior of the solution. In particular, by restricting our asymptotic result to solutions whose initial data are close to the initial profile of the stationary one-soliton, we obtain results on the asymptotic stability of the stationary one-solitons under any small perturbation in $H^{1,1}(\mathbb{R}_+)$. In the focusing case, such a result was already established by Deift and Park using different methods, and our work provides an alternative approach to obtain such results.
We consider a nonlinear Schr\"odinger equation with double power nonlinearity, where one power is focusing and mass critical and the other mass sub-critical. Classical variational arguments ensure that initial data with mass less than the mass of the ground state of the mass critical problem lead to global in time solutions. We are interested by the threshold dynamic and in particular by the existence of finite time blow up minimal solutions. For the mass critical problem, such an object exists thanks to the explicit conformal symmetry, and is in fact unique. For the focusing double power nonlinearity, we exhibit a new class of minimal blow up solutions with blow up rates deeply affected by the double power nonlinearity. The analysis adapts the recent approach developed by Rapha\"el and Szeftel for the construction of minimal blow up elements.
We constrain the primordial non-Gaussianity parameter of the local model f_{NL} using the skewness power spectrum associated with the two-to-one cumulant correlator of cosmic microwave background temperature anisotropies. This bispectrum-related power spectrum was constructed after weighting the temperature map with the appropriate window functions to form an estimator that probes the multipolar dependence of the underlying bispectrum associated with the primordial non-Gaussianity. We also estimate a separate skewness power spectrum sensitive more strongly to unresolved point sources. When compared to previous attempts at measuring the primordial non-Gaussianity with WMAP data, our estimators have the main advantage that we do not collapse information to a single number. When model fitting the two-to-one skewness power spectrum we make use of bispectra generated by the primordial non-Gaussianity, radio point sources, and lensing-secondary correlation. We analyze Q, V and W-band WMAP 5-year data using the KQ75 mask out to l_{max}=600. Using V and W-band data and marginalizing over model parameters related to point sources and lensing-secondary bispectrum, our overall and preferred constraint on f_{NL} is 11.0\pm23.7 at the 68% confidence level (-36.4 < f_{NL} < 58.4 at 95% confidence). We find no evidence for a non-zero value of f_{NL} even marginally at the 1\sigma level.
We consider a commutative algebra $\mathbb{B}$ over the field of complex numbers with a basis $\{e_1,e_2\}$ satisfying the conditions $(e_1^2+e_2^2)^2=0$, $e_1^2+e_2^2\ne 0$. Let $D$ be a bounded domain in the Cartesian plane $xOy$ and $D_{\zeta}=\{xe_1+ye_2 : (x,y)\in D\}$. Components of every monogenic function $\Phi(xe_1+ye_2)=U_{1}(x,y)\,e_1+U_{2}(x,y)\,ie_1+ U_{3}(x,y)\,e_2+U_{4}(x,y)\,ie_2$ having the classic derivative in $D_{\zeta}$ are biharmonic functions in $D$, i.e. $\Delta^{2}U_{j}(x,y)=0$ for $j=1,2,3,4$. We consider a Schwarz-type boundary value problem for monogenic functions in a simply connected domain $D_{\zeta}$. This problem is associated with the following biharmonic problem: to find a biharmonic function $V(x,y)$ in the domain $D$ when boundary values of its partial derivatives $\partial V/\partial x$, $\partial V/\partial y$ are given on the boundary $\partial D$. Using a hypercomplex analog of the Cauchy type integral, we reduce the mentioned Schwarz-type boundary value problem to a system of integral equations on the real axes and establish sufficient conditions under which this system has the Fredholm property.