ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study deformation theory of elliptic fibre bundles over curves in positive characteristics. As applications, we give examples of non-liftable elliptic surfaces in charactertic two and three, which answers a question of Katsura and Ueno. Also, we construct a class of elliptic fibrations, whose liftability is equivalent to a conjecture of F. Oort concerning the liftability of automorphisms of curves. Finally, we classify deformations of bielliptic surfaces.
In this paper, we study the Iwasawa theory of a motive whose Hodge-Tate weights are $0$ or $1$ (thence in practice, of a motive associated to an abelian variety) at a non-ordinary prime, over the cyclotomic tower of a number field that is either totally real or CM. In particular, under certain technical assumptions, we construct Sprung-type Coleman maps on the local Iwasawa cohomology groups and use them to define integral $p$-adic $L$-functions and (one unconditionally and other conjecturally) cotorsion Selmer groups. This allows us to reformulate Perrin-Riou's main conjecture in terms of these objects, in the same fashion as Kobayashi's $\pm$-Iwasawa theory for supersingular elliptic curves. By the aid of our theory of Coleman-adapted Kolyvagin systems that we develop here, we deduce parts of Perrin-Riou's main conjecture from an explicit reciprocity conjecture.
We report the AGILE gamma-ray observations and the results of the multiwavelength campaigns on seven flaring blazars detected by the mission: During two multiwavelength campaigns, we observed gamma-ray activity from two Flat Spectrum Radio Quasars of the Virgo region, e.g. 3C 279 and 3C 273 (the latter being the first extragalactic source simultaneously observed with the gamma-ray telescope and the hard X ray imager of the mission). Due to the large FOV of the AGILE/GRID instrument, we achieved an almost continuous coverage of the FSRQ 3C 454.3. The source showed flux above 10E-6 photons/cm2/s (E > 100 MeV) and showed day by day variability during all the AGILE observing periods. In the EGRET era, the source was found in high gamma-ray activity only once. An other blazar, PKS 1510-089 was frequently found in high gamma-ray activity. S5 0716+71, an intermediate BL Lac object, exhibited a very high gamma-ray activity and fast gamma-ray variability during a period of intense optical activity. We observed high gamma-ray activity from W Comae, a BL Lac object, and Mrk 421, an high energy peaked BL Lac object. For this source, a multiwavelength campaign from optical to TeV has been performed.
A simple test for time-asymmetry is devised and carried out on the brightest gamma-ray bursts detected by the Burst and Transient Source Experiment (BATSE) on board the {\it Compton} Gamma Ray Observatory. We show evidence that individual bursts are time-asymmetric on all time scales tested, from a time scale shorter than that of pulses which compose GRBs to a time scale similar to a greater envelope that contains these pulses. We also find bursts which manifest significant asymmetry only on time scales comparable to the duration of burst, and bursts for which no clear asymmetry on any time scale is present. The sense of the asymmetry is that bursts and/or component structures rise in a shorter time than they decay. We also find that our whole sample of bursts taken together is time- asymmetric, in that there are significantly more bursts and pulses where the rise is more rapid than the decay, on all time scales tested and for all energy bands tested. When our whole GRB sample is binned at 64-ms and integrated over all BATSE energies, the statistical significance is at the 6 $\sigma$ level. Models that predict time-symmetry are therefore excluded.
We explore a scenario where metal poor globular clusters (GCs) form at the centres of their own dark matter halos in the early universe before reionization. This hypothesis leads to predictions about the abundance, distribution and kinematics of GCs today that we explore using cosmological N-body simulations and analytical modelling. We find that selecting the massive tail of collapsed objects at $z\gtrsim 9$ as GC formation sites leads to four main predictions: i) a highly clustered population of GCs around galaxies today, ii) a natural scaling between number of GCs and halo virial mass that follows roughly the observed trend, iii) a very low number of free floating GCs outside massive halos and iv) GCs should be embedded within massive and extended dark matter (sub)halos. We find that the strongest constraint to the model is given by the combination of (i) and (ii): a mass cut to tagged GCs halos which accounts for the number density of metal poor GCs today predicts a radial distribution that is too extended compared to recent observations. On the other hand, a mass cut sufficient to match the observed half number radius could only explain 60% of the metal poor population. In all cases, observations favour early redshifts for GC formation ($z\geq 15$).
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played by the extension to the framework of non-commutative geometry of the permutation of two copies of $\Omega^1$. The construction of the linear connection as well as the definition of torsion and curvature is first proposed in the setting of the derivations based differential calculus of Dubois- Violette and then a generalisation to the framework proposed by Connes as well as other non-commutative differential calculi is suggested. The covariant derivative obtained admits an extension to the tensor product of several copies of $\Omega^1$. These constructions are illustrated with the example of the algebra of $ n \times n$ matrices.
Consider the coupon collector problem where each box of a brand of cereal contains a coupon and there are n different types of coupons. Suppose that the probability of a box containing a coupon of a specific type is $1/n$ and that we keep buying boxes until we collect at least $m$ coupons of each type. For $k\geq m$ call a certain coupon a $k$-ton if we see it $k$ times by the time we have seen $m$ copies of all of the coupons. Here we determine the asymptotic distribution of the number of $k$-tons after we have collected $m$ copies of each coupon for any $k$ in a restricted range, given any fixed $m$. We also determine the asymptotic joint probability distribution over such values of $k$ and the total number of coupons collected.
A model lattice ab initio parameterised Hamiltonian spanning a broad range of alloy compositions and a large variety of chemical and magnetic configurations has been developed for face-centered cubic Fe-Ni alloys. Thermodynamic and magnetic properties of the alloys are explored using configuration and magnetic Monte Carlo simulations in a temperature range extending well over 1000 K.
There is an important parameter in control theory which is closely related to the directed matching ratio of the network, as shown by Liu, Slotine and Barab\'asi (2011). We give proofs on two main statements of that paper on the directed matching ratio, which were based on numerical results and heuristics from statistical physics. First, we show that the directed matching ratio of directed random networks given by a fix sequence of degrees is concentrated around its mean. We also examine the convergence of the (directed) matching ratio of a random (directed) graph sequence that converges in the local weak sense, and generalize the result of Elek and Lippner (2009). We prove that the mean of the directed matching ratio converges to the properly defined matching ratio parameter of the limiting graph. We further show the almost sure convergence of the matching ratios for the most widely used families of scale-free networks, which was the main motivation of Liu, Slotine and Barab\'asi.
Pseudobinary heterostructural alloys of ZnO with MgO or CdO are studied by composing the system locally of clusters with varying ratio of cations. We investigate fourfold (wurtzite structure) and sixfold (rocksalt structure) coordination of the atoms. By means of density functional theory we study a total number of 256 16-atom clusters divided into 22 classes for the wurtzite structure and 16 classes for the rocksalt structure for each of the alloy systems. The fraction with which each cluster contributes to the alloy is determined for a given temperature T and composition x within (i) the generalized quasi-chemical approximation, (ii) the model of a strict-regular solution, and (iii) the model of microscopic decomposition. From the cluster fractions we derive conclusions about the miscibility and the critical compositions at which the average crystal structure changes. Thermodynamic properties such as the mixing free energy and the mixing entropy are investigated for the three different statistics. We discuss the consequences of the two different local lattice structures for characteristic atomic distances, cohesive energies, and the alloys' elasticities. The differences in the properties of Mg_x Zn_{1-x} O and Cd_x Zn_{1-x} O are explained and discussed.
We investigate response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like the XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasista- tionary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with zero-means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for the skew-normal distribution functions.
The application of higher-order Laguerre Gauss (LG) modes in large-scale gravitational wave detectors has recently been proposed. In comparison to the fundamental mode, some higher-order Laguerre Gauss modes can significantly reduce the contribution of coating Brownian noise. Using frequency domain simulations we give a detailed analysis of the longitudinal and angular control signals derived with a LG33 mode in comparison to the fundamental TEM00 mode. The performance regarding interferometric sensing and control of the LG33 mode is found to be similar, if not even better in all aspects of interest. In addition, we evaluate the sensitivity gain of the implementation of LG33 modes into the Advanced Virgo instrument. Our analysis shows that the application of the LG33 mode results in a broadband improvement of the Advanced Virgo sensitivity, increasing the potential detection rate of binary neutron star inspirals by a factor 2.1.
We study out-of equilibrium properties of a quantum dot in a GaAs/AlGaAs two-dimensional electron gas. By means of single electron counting experiments, we measure the distribution of work and dissipated heat of the driven quantum dot and relate these quantities to the equilibrium free energy change, as it has been proposed by C. Jarzynski [Phys. Rev. Lett. {\bf78}, 2690 (1997)]. We discuss the influence of the degeneracy of the quantized energy state on the free energy change as well as its relation to the tunnel rates between the dot and the reservoir.
Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability distribution of their appearance. This article mainly addresses studies in toroidal compactifications with magnetic fluxes.
In this work, archive 1.4 and 4.86 GHz radio continuum data from the VLA were re-reduced and, together with the 1.4 GHz maps from the NVSS, investigated for the presence of a detectable, non-thermal continuum radio emission that could be associated with the TDG candidates in HCG 26, 91, and 96. Radio emission highly coincident with the optical and $\rm H_{\alpha}$ emission maxima of the TDG candidate HCG 91i (estimated physical separation of less than 150 pc) was revealed. Should this emission be intrinsic to this object, it would imply the presence of a magnetic field as strong as 11--16 $\mu$G -- comparable to that found in the most radio-luminous, star-forming dwarf galaxies of non-tidal origin. However, the star formation rate derived for this object using the radio flux is about two orders of magnitude higher, than the one estimated from the $\rm H_{\alpha}$ data. Analysis of the auxiliary radio, ultraviolet and infrared data suggests that either the radio emission originates in a background object with an aged synchrotron spectrum (possibly a GHz-peaked source), or the $\rm SFR_{H_{\alpha}}$ estimate is lower due to the fact that it traces the most recent star formation, while most of the detected radio emission originated when what is known as HCG 91i was still a part of its parent galaxy. The latter scenario is supported by a very large stellar mass derived from 3.6 and 4.5 $\mu$m data, implying high star formation in the past.
We study conjectures on the dimension of linear systems on the blow-up of P^2 and P^3 at points in very general position. We provide algorithms and Maple codes based on these conjectures.
Interacting binaries typically have separations in the milli-arcsecond regime and hence it has been challenging to resolve them at any wavelength. However, recent advances in optical interferometry have improved our ability to discern the components in these systems and have now enabled the direct determination of physical parameters. We used the Navy Prototype Optical Interferometer to produce for the first time images resolving all three components in the well-known Algol triple system. Specifically, we have separated the tertiary component from the binary and simultaneously resolved the eclipsing binary pair, which represents the nearest and brightest eclipsing binary in the sky. We present revised orbital elements for the triple system, and we have rectified the 180-degree ambiguity in the position angle of Algol C. Our directly determined magnitude differences and masses for this triple star system are consistent with earlier light curve modeling results.
We observe that the state space of Landau-Ginzburg isolated singularities is simply a special case of Chen-Ruan orbifold cohomology relative to the generic fibre of the potential. This leads to the definition of the cohomology of hybrid Landau-Ginzburg models and its identification via an explicit isomorphism to the cohomology of Calabi-Yau complete intersections inside weighted projective spaces. The combinatorial method used in the case of hypersurfaces proven by the first named author in collaboration with Ruan is streamlined and generalised after an orbifold version of the Thom isomorphism and of the Tate twist.
We provide a detailed mathematical analysis of a model for phase separation on biological membranes which was recently proposed by Garcke, R\"atz, R\"oger and the second author. The model is an extended Cahn-Hilliard equation which contains additional terms to account for the active transport processes. We prove results on the existence and regularity of solutions, their long-time behaviour, and on the existence of stationary solutions. Moreover, we investigate two different asymptotic regimes. We study the case of large cytosolic diffusion and investigate the effect of an infinitely large affinity between membrane components. The first case leads to the reduction of coupled bulk-surface equations in the model to a system of surface equations with non-local contributions. Subsequently, we recover a variant of the well-known Ohta-Kawasaki equation as the limit for infinitely large affinity between membrane components.
By combining temperature-dependent resistivity and Hall effect measurements, we investigate donor state energy in Si-doped \b{eta}-Ga2O3 films grown using metal-organic vapor phase epitaxy (MOVPE). High magnetic field Hall effect measurements (H = +/-90 kOe) showed non-linear Hall resistance for T < 150 K revealing two-band conduction. Further analyses revealed carrier freeze-out characteristics in both bands yielding donor state energies of ~ 33.7 and ~ 45.6 meV. The former is consistent with the donor energy of Si in \b{eta}-Ga2O3 whereas the latter suggests a residual donor state, likely associated with a DX center. This study provides a critical insight into the impurity band conduction and the defect energy states in \b{eta}-Ga2O3 using high-field magnetotransport measurements.
We present a physical model for electronic switching in cantilever based nano-electro-mechanical field effect transistors, focusing on the steepness of its switching curve. We find that the subthreshold swing of the voltage transfer characteristic is governed by two separate considerations - the ability of the charges to correlate together through dipolar interactions and amplify the active torque, versus the active pull-in forces that drive an abrupt phase transition and close the air gap between the tip of the cantilever and the drain. For small sized relays, dipolar and short-range Van Der Waals 'sticking' forces dominate, while for longer cantilevers the capacitive energy acquires a major role. The individual pull-in and pull-out phases demonstrate a remarkably low subthreshold swing driven by the capacitive forces, sharpened further by dipolar correlation. The sharp switching, however, comes at the expense of strong hysteresis as the metastable and stable states interchange along the forward and reverse phases of the voltage scan.
We report on high-resolution acoustic, specific-heat and thermal expansion measurements in the vicinity of the antiferromagnetic phase transition at T_N = 1.88 K on a high-quality single crystal of the natural mineral azurite. A detailed investigation of the critical contribution to the various quantities at T_N is presented. The set of critical exponents and amplitude ratios of the singular contributions above and below the transition indicate that the system can be reasonably well described by a three-dimensional Heisenberg antiferromagnet.
Magnetoelectric (ME) interactions in layered structures of magnetostrictive and piezoelectric phases are mediated by mechanical deformation. Here we discuss the frequency dependence of ME coupling in bilayers and trilayers of Permendur, a ferromagnetic alloy, and lead zirconate titanate. Data on ME voltage coefficient versus frequency profiles reveal a giant ME coupling at electromechanical resonance. The maximum voltage coefficient of 90 V/cm Oe is three orders of magnitude higher than low-frequency values. The ME interactions for transverse fields is an order of magnitude stronger than for longitudinal fields. These results are in agreement with theory. The resonance ME effect, therefore, is a novel tool for enhancing the magnetic-to-electric field conversion efficiency in the composites.
We investigate two distinct universality classes for probe particles that move stochastically in a one-dimensional driven system. If the random force that drives the probe particles is fully generated by the current fluctuations of the driven fluid, such as when the probe particles are embedded in a ring, they inherit the dynamical exponent of the fluid, which generically is z=3/2. On the other hand, if the random force has a part that is temporally uncorrelated, the resulting motion can be described by a dynamical exponent z=2 as considered in previous work.
We have performed point contact spectroscopy measurements on a sample constituted by a metallic ferromagnetic oxide (SrRuO_3) bottom electrode and a tunnel ferrimagnetic (CoFe_2O_4) barrier. Andreev reflection is observed across the tunnel barrier. From the comparison of Andreev reflection in SrRuO3 and across the CoFe_2O_4 barrier we infer that the ferrimagnetic barrier has a spin filter efficiency not larger than +13%. The observation of a moderate and positive spin filtering is discussed in the context of the microstructure of the barriers and symmetry-related spin filtering effects.
In this paper, we study the defocusing energy-critical nonlinear Schr\"odinger equations $$ i\partial_t u + \Delta u = |u|^{\frac{4}{d-2}} u. $$ When $d=3,4$, we prove the almost sure scattering for the equations with non-radial data in $H_x^s$ for any $s\in\mathbb{R}$. In particular, our result does not rely on any spherical symmetry, size or regularity restrictions.
The question has been solved whether Bell's inequalities cover all possible kinds of hidden-variable theories. It has been shown that the given nequalities can be hardly derived when the changing space position of photon-pair source together with the microscopic space structure of measuring devices are taken into account; and when corresponding impact parameters (i.e., exact impact points) of photons in individual measuring devices (polarizers) influence measured values, in addition to usually considered characteristics.
We analysed archival spectroscopic data of AM CVn taken with the William Herschel Telescope in 1996. In the literature two orbital periods for AM CVn are proposed. A clear S-wave in the HeI 4471, 4387 and 4143 \AA lines is revealed when the spectra are folded on the 1029 s period. No signature of this S-wave is seen when folded on 1051 s. Doppler tomography of the line profiles shows a clear signature of the hotspot. Using this we can constrain the value of K_2 to lie between 210 and 280 km/s. Our work confirms the binary nature of AM CVn beyond any doubt, establishes 1028.73 s as the true orbital period and supports the interpretation of AM CVn as a permanent superhump system.
We consider quenched and annealed Lyapunov exponents for the Green's function of $-\Delta+\gamma V$, where the potentials $V(x), x\in\Z^d$, are i.i.d. nonnegative random variables and $\gamma>0$ is a scalar. We present a probabilistic proof that both Lyapunov exponents scale like $c\sqrt{\gamma}$ as $\gamma$ tends to 0. Here the constant $c$ is the same for the quenched as for the annealed exponent and is computed explicitly. This improves results obtained previously by Wei-Min Wang. We also consider other ways to send the potential to zero than multiplying it by a small number.
For primes p greater than 3, we propose a conjecture that relates the values of cup products in the Galois cohomology of the maximal unramified outside p extension of a cyclotomic field on cyclotomic p-units to the values of p-adic L-functions of cuspidal eigenforms that satisfy mod p congruences with Eisenstein series. Passing up the cyclotomic and Hida towers, we construct an isomorphism of certain spaces that allows us to compare the value of a reciprocity map on a particular norm compatible system of p-units to what is essentially the two-variable p-adic L-function of Mazur and Kitagawa.