ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use Altmann's toric fan description of P-resolutions to formulate a new description of deformation theory invariants for two-dimensional cyclic quotient singularities. In particular, we show how to calculate the dimensions of the (reduced) versal base space components as well as Milnor numbers of smoothings over them.
In this paper we show an abstract theorem involving the existence of critical points for a functional $I$, which permit us to prove the existence of solutions for a large class of Berestycki-Lions type problems. In the proof of the abstract result we apply the deformation lemma on a special set associated with $I$, which we call of Pohozaev set.
Based on the work of Gritsenko et al. (GLLB) [Phys. Rev. A 51, 1944 (1995)], the method of Kuisma et al. [Phys. Rev. B 82, 115106 (2010)] to calculate the band gap in solids was shown to be much more accurate than the common local density approximation (LDA) and generalized gradient approximation (GGA). The main feature of the GLLB-SC potential (SC stands for solid and correlation) is to lead to a nonzero derivative discontinuity that can be conveniently calculated and then added to the Kohn-Sham band gap for a comparison with the experimental band gap. In this work, a thorough comparison of GLLB-SC with other methods, e.g., the modified Becke-Johnson (mBJ) potential [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)], for electronic, magnetic, and density-related properties is presented. It is shown that for the band gap, GLLB-SC does not perform as well as mBJ for systems with a small band gap and strongly correlated systems, but is on average of similar accuracy as hybrid functionals. The results on itinerant metals indicate that GLLB-SC overestimates significantly the magnetic moment (much more than mBJ does), but leads to excellent results for the electric field gradient, for which mBJ is in general not recommended. In the aim of improving the results, variants of the GLLB-SC potential are also tested.
Located in the Small Magellanic Cloud (SMC), SXP214 is an X-ray pulsar in a high mass X-ray binary system with a Be-star companion. A recent survey of the SMC under a Chandra X-ray Visionary program found the source in a transition when the X-ray flux was on a steady rise. The Lomb-Scargle periodogram revealed a pulse period of 211.49 +/- 0.42 s, which is significantly (>5sigma) shorter than the previous measurements with XMM-Newton and RXTE. This implies that the system has gone through sudden spin-up episodes recently. The pulse profile shows a sharp eclipse-like feature with a modulation amplitude of >95%. The linear rise of the observed X-ray luminosity from <~2x to 7x10^35 erg s^-1 is correlated with steady softening of the X-ray spectrum, which can be described by the changes in the local absorption from N_H ~ 10^24 to <~10^20 cm^-2 for an absorbed power-law model. The soft X-ray emission below 2 keV was absent in the early part of the observation when only the pulsating hard X-ray component was observed, whereas at later times both soft and hard X-ray components were observed pulsating. A likely explanation is that the neutron star was initially hidden in the circumstellar disk of the companion, and later came out of the disk with the accreted material that continued fueling the observed pulsation.
In this work, we find new static, spherically symmetric, dyonic, globally regular exact solutions to $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory with a negative cosmological constant $\Lambda$, in the regime that $|\Lambda|$ is very large. In this regime, we also prove that dyonic globally regular solutions may be uniquely characterised by a countably infinite set of effective global charges; and that dyon solutions may be distinguished from dyonic black hole solutions to the same field equations by their ADM masses. These solutions have potential modelling applications for certain exotic gravitational objects.
Berezinskii-Kosterlitz-Thouless (BKT) transition, the transition of the 2D sine-Gordon model, plays an important role in the low dimensional physics. We relate the operator content of the BKT transition to that of the SU(2) Wess-Zumino-Witten model, using twisted boundary conditions. With this method, in order to determine the BKT critical point, we can use the level crossing of the lower excitations than the periodic boundary case, thus the convergence to the transition point is highly improved. Then we verify the efficiency of this method by applying to the S=1,2 spin chains.
We present spectroscopic confirmation of three new two-image gravitationally lensed quasars, compiled from existing strong lens and X-ray catalogs. Images of HSC J091843.27$-$022007.5 show a red galaxy with two blue point sources at either side, separated by 2.26 arcsec. This system has a source and a lens redshifts $z_s=0.804$ and $z_{\ell}=0.459$, respectively, as obtained by our follow-up spectroscopic data. CXCO J100201.50$+$020330.0 shows two point sources separated by 0.85 arcsec on either side of an early-type galaxy. The follow-up spectroscopic data confirm the fainter quasar has the same redshift with the brighter quasar from the SDSS fiber spectrum at $z_s=2.016$. The deflecting foreground galaxy is a typical early-type galaxy at a redshift of $z_{\ell}=0.439$. SDSS J135944.21$+$012809.8 has two point sources with quasar spectra at the same redshift $z_s=1.096$, separated by 1.05 arcsec, and fits to the HSC images confirm the presence of a galaxy between these. These discoveries demonstrate the power of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP)'s deep imaging and wide sky coverage. Combined with existing X-ray source catalogues and follow-up spectroscopy, the HSC-SSP provides us unique opportunities to find multiple-image quasars lensed by a foreground galaxy.
It is possible to fabricate mesoscopic structures where at least one of the dimensions is of the order of de Broglie wavelength for cold electrons. By using semiconductors, composed of more than one material combined with a metal slip-gate, two-dimensional quantum tubes may be built. We present a method for predicting the transmission of low-temperature electrons in such a tube. This problem is mathematically related to the transmission of acoustic or electromagnetic waves in a two-dimensional duct. The tube is asymptotically straight with a constant cross-section. Propagation properties for complicated tubes can be synthesised from corresponding results for more simple tubes by the so-called Building Block Method. Conformal mapping techniques are then applied to transform the simple tube with curvature and varying cross-section to a straight, constant cross-section, tube with variable refractive index. Stable formulations for the scattering operators in terms of ordinary differential equations are formulated by wave splitting using an invariant imbedding technique. The mathematical framework is also generalised to handle tubes with edges, which are of large technical interest. The numerical method consists of using a standard MATLAB ordinary differential equation solver for the truncated reflection and transmission matrices in a Fourier sine basis. It is proved that the numerical scheme converges with increasing truncation.
In this paper, we establish two mean value theorems for the number of solutions of the Diophantine equation $\frac{a}{n}=\frac{1}{x}+\frac{1}{y}$, in the case when $a$ is fixed and $n$ varies and in the case when both $a$ and $n$ vary.
Aims: We employ archival Spitzer slit-scan observations of the HH211 outflow in order to investigate its warm gas content, assess the jet mass flux in the form of H2 and probe for the existence of an embedded atomic jet. Methods: Detected molecular and atomic lines are interpreted by means of emission line diagnostics and an existing grid of molecular shock models. The physical properties of the warm gas are compared against other molecular jet tracers and to the results of a similar study towards the L1448-C outflow. Results: We have detected and mapped the v=0-0 S(0) - S(7) H2 lines and fine-structure lines of S, Fe+, and Si+. H2 is detected down to 5" from the source and is characterized by a "cool" T~300K and a "warm" T~1000 K component, with an extinction Av ~ 8 mag. The amount of cool H2 towards the jet agrees with that estimated from CO assuming fully molecular gas. The warm component is well fitted by C-type shocks with a low beam filling factor ~ 0.01-0.04 and a mass-flux similar to the cool H2. The fine-structure line emission arises from dense gas with ionization fraction ~0.5 - 5 x 10e-3, suggestive of dissociative shocks. Line ratios to sulfur indicate that iron and silicon are depleted compared to solar abundances by a factor ~10-50. Conclusions: Spitzer spectral mapping observations reveal for the first time a cool H$_2$ component towards the CO jet of HH211 consistent with the CO material being fully molecular and warm at ~ 300 K. The maps also reveal for the first time the existence of an embedded atomic jet in the HH211 outflow that can be traced down to the central source position. Its significant iron and silicon depletion excludes an origin from within the dust sublimation zone around the protostar. The momentum-flux seems insufficient to entrain the CO jet, although current uncertainties on jet speed and shock conditions are too large for a definite conclusion.
The dynamical phase diagram of the fractional Langevin equation is investigated for harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) $\alpha_c=0.402\pm 0.002$ marks a transition to a non-monotonic under-damped phase, (ii) $\alpha_R=0.441...$ marks a transition to a resonance phase when an external oscillating field drives the system, (iii) $\alpha_{\chi_1}=0.527...$ and (iv) $\alpha_{\chi_2}=0.707...$ marks transition to a double peak phase of the "loss" when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over-damped, under-damped regimes, motion and resonances, show behaviors different from normal.
We have observed commensurability oscillations (CO) in the Hall resistance $R_{yx}$ of a unidirectional lateral superlattice (ULSL). The CO, having small amplitudes ($\sim$ 1 $\Omega$) and being superposed on a roughly three-orders of magnitude larger background, are obtained by directly detecting the difference in $R_{yx}$ between the ULSL area and the adjacent unmodulated two-dimensional electron gas area, and then extracting the odd part with respect to the magnetic field. The CO thus obtained are compared with a theoretical calculation and turn out to have the amplitude much smaller than the theoretical prediction. The implication of the smaller-than-predicted CO in $R_{yx}$ on the thermoelectric power of ULSL is briefly discussed.
We study the regularity and behavior at the origin of solutions to the two-dimensional degenerate Monge-Ampere equation with homogeneous right hand side of degree alpha, alpha>-2. We show that when alpha > 0, solutions admit only two possible behaviors near the origin, radial and non-radial. We also show that the radial behavior is unstable. For alpha<0 we prove that solutions admit only the radial behavior near the origin.
In this work we study the homogenization problem for nonlinear eigenvalues of quasilinear elliptic operators. We obtain an explicit order of convergence in $k$ and in $\varepsilon$ for the (variational) eigenvalues.
We conduct a multi-wavelength morphological study of the Galactic supernova remnant RXJ0852.0-4622 (also known as Vela Jr., Vela Z and G266.2-1.2). RX J0852.0-4622 is coincident with the edge of the larger Vela supernova remnant causing confusion in the attribution of some filamentary structures to either RX J0852.0-4622 or its larger sibling. We find that the RX J0852.0-4622 radio continuum emission can be characterised by a 2-dimensional shell with a radius of 0.90+/-0.01deg (or 11.8+/-0.6pc at an assumed distance of 750pc) centred at (l,b)=(133.08+/-0.01 deg,-46.34+/-0.01deg) (or RA=8h52m19.2s, Dec=-46deg20'24.0'', J2000), consistent with X-ray and gamma-ray emission. Although [OIII] emission features are generally associated with the Vela SNR, one particular [OIII] emission feature, which we denote as "the Vela Claw", morphologically matches a molecular clump that is thought to have been stripped by the stellar progenitor of the RX J0852.0-4622 SNR. We argue that the Vela Claw feature is possibly associated with RX J0852.0-4622. Towards the north-western edge of RX J0852.0-4622, we find a flattening of the radio spectral index towards another molecular clump also thought to be associated with RX J0852.0-4622. It is currently unclear whether this feature and the Vela Claw result from interactions between the RX J0852.0-4622 shock and the ISM.
A general theory is developed to describe graphene with arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the minimal conductivity of graphene with resonant scatterers. In the case of smooth resonant impurities conductivity grows logarithmically with increasing impurity concentration, in agreement with renormalization group analysis for the symmetry class DIII. For vacancies (or strong on-site potential impurities) the conductivity saturates at a constant value that depends on the vacancy distribution among two sublattices as expected for the symmetry class BDI.
We study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefolds and the subgroup of the N\'eron-Severi group generated by these sections is not finitely generated. This also gives examples of K3 surfaces over the function field F of a complex curve with Zariski dense F-rational points, whose geometric model is Calabi-Yau.
In this paper we obtain the formal asymptotic expansion of the logarithms $\ln p_s(\alpha)$ of $p_s(\alpha)$, which are canonical continuations of polynomials of binomial type $p_n(\alpha)$. Our approach is based on linear methods which do not require the calculation of expansions $(p_s(\alpha)\alpha^{-s}-1)^k$, as opposed to the direct logarithmization.
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The quantum Hilbert space is constructed from the parameters of the various experiments using group representation theory. It is shown under natural assumptions that a subset of the set of unit vectors of this space, the generalized coherent state vectors, can be put in correspondence with questions of the kind: What is the value of the (complete) parameter? - together with a crisp answer to that question. Links are made to statistical models in general, to model reduction of overparametrized models and to the design of experiments. It turns out to be essential that the range of the statistical parameter is an invariant set under the relevant symmetry group.
We discuss a toy model for an emergent non-relativistic gravitational theory. Within a certain class of Bose-Einstein condensates, it is possible to show that, in a suitable regime, a modified version of non-relativistic Newtonian gravity does effectively describes the low energy dynamics of the coupled system condensate/quasi-particles.
By relaxing the regularity conditions imposed in arXiv:1107.1722 on half-BPS solutions to six-dimensional Type~4b supergravity, we enlarge the space of solutions to include two new half-BPS configurations, which we refer to as the \kap\ and the \funnel. We give evidence that the \kap\ and \funnel\ can be interpreted as fully back-reacted brane solutions with respectively $AdS_2$ and $AdS_2\times S^2$ world volumes. \kap\ and \funnel\ solutions with a single asymptotic $AdS_3 \times S^3$ region are constructed analytically. We argue that \kap\ solutions provide simple examples of holographic duals to boundary CFTs in two dimensions and present calculations of their holographic boundary entropy to support the BCFT dual picture.
Using the Keldysh Green function technique, we calculate the finite-frequency correlator between the electrical current and the heat current flowing through a quantum dot connected to reservoirs. At equilibrium, we find that this quantity, called mixed noise, is linked to the thermoelectric ac-conductance by the fluctuation-dissipation theorem. Out-of-equilibrium, we discuss its spectrum and find evidence of the close relationship between the mixed noise and the thermopower. We study the spectral coherence and identify the conditions to have a strong correlation between the electrical and heat currents. The change in the spectral coherence due to the presence of a temperature gradient between the reservoirs is also highlighted.
We investigate the viability of thermal leptogenesis in type-I seesaw models with leptonic flavour symmetries that lead to tribimaximal neutrino mixing. We consider an effective theory with an A4 x Z3 x Z4 symmetry, which is spontaneously broken at a scale much higher than the electroweak scale. At the high scale, leptonic Yukawa interactions lead to exact tribimaximal mixing and the heavy Majorana neutrino mass spectrum is exactly degenerate. In this framework, leptogenesis becomes viable once this degeneracy is lifted either by renormalization group effects or by a soft breaking of the A4 symmetry. The implications for low-energy neutrino physics are discussed.
We analyzed the influence of static gravitational field on the vacuum and proposed the concept of inhomogeneous vacuum. According to the corresponding Fermat's principle in the general relativity, we derived a graded refractive index of vacuum in a static gravitational field. We found that the light deflection in a gravitational field can be calculated correctly with the use of this refractive index and therefore the gravitational lensing can be treated conveniently with the optical method. For illustration, we simulated the imaging of gravitational lensing, figured out the time delay between the two images and calculated the lens mass in a conventional optical way.
In this work we extend previous work on the evolution of a Primordial Black Hole (PBH) to address the presence of a dark energy component with a super-negative equation of state as a background, investigating the competition between the radiation accretion, the Hawking evaporation and the phantom accretion, the latter two causing a decrease on black hole mass. It is found that there is an instant during the matter-dominated era after which the radiation accretion becomes negligible compared to the phantom accretion. The Hawking evaporation may become important again depending on a mass threshold. The evaporation of PBHs is quite modified at late times by these effects, but only if the Generalized Second Law of thermodynamics is violated.
We measure the UV-optical color dependence of galaxy clustering in the local universe. Using the clean separation of the red and blue sequences made possible by the NUV - r color-magnitude diagram, we segregate the galaxies into red, blue and intermediate "green" classes. We explore the clustering as a function of this segregation by removing the dependence on luminosity and by excluding edge-on galaxies as a means of a non-model dependent veto of highly extincted galaxies. We find that \xi (r_p, \pi) for both red and green galaxies shows strong redshift space distortion on small scales -- the "finger-of-God" effect, with green galaxies having a lower amplitude than is seen for the red sequence, and the blue sequence showing almost no distortion. On large scales, \xi (r_p, \pi) for all three samples show the effect of large-scale streaming from coherent infall. On scales 1 Mpc/h < r_p < 10 Mpc/h, the projected auto-correlation function w_p(r_p) for red and green galaxies fits a power-law with slope \gamma ~ 1.93 and amplitude r_0 ~ 7.5 and 5.3, compared with \gamma ~ 1.75 and r_0 ~ 3.9 Mpc/h for blue sequence galaxies. Compared to the clustering of a fiducial L* galaxy, the red, green, and blue have a relative bias of 1.5, 1.1, and 0.9 respectively. The w_p(r_p) for blue galaxies display an increase in convexity at ~ 1 Mpc/h, with an excess of large scale clustering. Our results suggest that the majority of blue galaxies are likely central galaxies in less massive halos, while red and green galaxies have larger satellite fractions, and preferentially reside in virialized structures. If blue sequence galaxies migrate to the red sequence via processes like mergers or quenching that take them through the green valley, such a transformation may be accompanied by a change in environment in addition to any change in luminosity and color.
Isoscalar (IS) monopole and dipole excitations in $^{16}$O were investigated by the method of shifted basis antisymmetrized molecular dynamics combined with the generator coordinate method. Significant strengths of the IS monopole and dipole transitions were obtained in the low-energy region below the giant resonances. In addition to the compressive mode, which mainly contributes to the high-energy strengths for the IS dipole giant resonance, we obtained a variety of low-energy dipole modes such as the vortical dipole mode in the $1^-_1$ state of the vibrating tetrahedral $4\alpha$ and the $^{12}$C+$\alpha$ cluster structure in the $1^-_2$ state. The $1^-_1$ state contributes to the significant low-energy strength of the IS dipole transition as 5\% of the energy-weighted sum rule, which describes well the experimental data observed by the $\alpha$ inelastic scattering.
Sect 1 introduces Nielsen classes attached to (G,C), where C is r conjugacy classes in a finite group G, and a braid action on them. These give reduced Hurwitz spaces, denoted H(G,C)^rd. The section concludes with a braid formula for the genus of these spaces when r = 4.   If there is at least one prime l for which G is divisible by l, but has no Z/l quotient, then there is a canonical tower of reduced Hurwitz spaces over H(G,C)^rd, using the Universal Frattini cover, ~G, of G, and ~G_ab, its abelianized version. The towers are nonempty assuming C are l' classes satisfying a cohomological condition from a lift invariant. A M(odular)T(ower) is a projective sequence of components of the canonical tower.   Sect 2 introduces the book [Fr18], which takes on generalizing Serre's O(pen)I(mage)T(heorem}, interpreted as the case when G is a dihedral group D_l and C is four repetitions of the involution conjugacy class. Serre's Theorem separated decomposition groups of projective sequences of points in the modular curve towers into two types: CM (complex multiplication) and GL_2. When r = 4, all MT levels are upper half-plane quotients ramified at 0 (of order 3), 1 (of order 2) and \infty (corresponding to the cusps). They are appropriate therefore to compare Serre's OIT with the cusps and decomposition group fibers. [Fr18] emphasizes new phenomena in cusps, and components, while still showing in high tower levels a valid comparison with modular curves.   It also aims to show how MTs can expand the applications usual for modular curve towers, recognizing those problems directly interpret from the Inverse Galois Problem. The l-adic representations of the title come from the abelianized version of the Universal Frattini cover.