ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider an elliptic Kolmogorov equation lambda u - Ku =f in a convex subset C of a separable Hilbert space X. We prove maximal Sobolev regularity of its weak solution, when lambda >0 and f is in L^2(C,nu), where nu is the log-concave measure associated to the system. Moreover we prove maximal estimates on the gradient of u, that allow to show that u satisfies the Neumann boundary condition in the sense of traces at the boundary of C. The general results are applied to Kolmogorov equations of reaction-diffusion stochastic PDEs and Cahn-Hilliard stochastic PDEs in convex sets of suitable Hilbert spaces.
Reliable data from the very recent high-precision measurements on the antiproton fluxes and the antiproton-to-proton ratios by the PAMELA Collaboration at relatively much higher energies are now available. The results with regard to antiproton production phenomena spring no special surprises; rather they are sharply in contrast with and contradiction to the case of positron production at the same energy-range. However, the totality of data on antiproton production from the past experiments to the very recent PAMELA outburst seem to be a very challenging exercise for interpretation in terms of the secondary production mechanisms alone, the galactic propagation model etc against the background of the `dark-matter'-related controversy. In the present work we assume the validity of the simple leaky box model, choose a simple particle production model and attempt at providing a comprehensive interpretation of the totality of data on both antiproton flux measurements and the $\overline{P}/P$ ratio-values for the various experiments ranging from BESS, CAPRICE to the latest PAMELA experiment. With the assumption of no contribution from the exotic sources to the antiproton production process, our model and the method describe the totality of the measured data with a fair degree of success.
We study combined interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases in a Josephson supercurrent of local and nonlocal (split) Cooper pairs. We analyze a junction between two superconductors interconnected through a normal-state nanostructure with either (i) a ring, where single-electron interference is possible, or (ii) two parallel nanowires, where the single-electron interference can be absent, but the cross Andreeev reflection can occur. In the low-transmission regime in both geometries the AB and AC effects can be related to only local or nonlocal Cooper pair transport, respectively.
Let $Sh_K(G,\mu)$ be a Shimura variety of KHT type, as introduced in Harris-Taylor book, associated to some similitude group $G/\mathbb Q$ and a open compact subgroup $K$ of $G(\mathbb A)$. For any irreducible algebraic $\overline{\mathbb Q}_l$-representation $\xi$ of $G$, let $V_\xi$ be the $\mathbb Z_l$-local system on $Sh_K(G,\mu)$. From my paper about p-stabilization, we know that if we allow the local component $K_l$ of $K$ to be small enough, then there must exists some non trivial cohomology classes with coefficient in $V_\xi$. The aim of this paper is then to construct explicitly such torsion classes with the control of $K_l$. As an application we obtain the construction of some new automorphic congruences between tempered and non tempered automorphic representations of the same weight and same level at $l$.
We have used the IRAM 30-m and FCRAO 14-m telescopes to observe the molecular clumps associated with 12 ultracompact (UC) HII regions in the J=6-5, 8-7 and 13-12 rotational transitions of methyl-acetylene (CH3C2H). Under the assumption of LTE and optically thin emission, we have derived temperature estimates ranging from 30 to 56 K. We estimate that the clumps have diameters of 0.2-1.6 pc, H_2 densities of 10^5-10^6 {cm^{-3}}, and masses of 10^2-2 10^4 M_\odot. We compare these values with those obtained by other authors from different molecular tracers and find that the H_2 density and the temperature inside the clumps vary respectively like n_{H_2} ~ R^{-2.6} and T ~ R^{-0.5}, with R distance from the centre. We also find that the virial masses of the clumps are ~3 times less than those derived from the CH3C2H column densities: we show that a plausible explanation is that magnetic fields play an important role to stabilise the clumps, which are on the verge of gravitational collapse. Finally, we show that the CH3C2H line width increases for decreasing distance from the clump centre: this effect is consistent with infall in the inner regions of the clumps. We conclude that the clumps around UC HII regions are likely to be transient (~10^(5) yr) entities, remnants of isothermal spheres currently undergoing gravitational collapse: the high mass accretion rates (~10^{-2} M_\odot yr^{-1}) lead to massive star formation at the centre of such clumps.
Magic angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless low-energy bands and the ability to tune the band filling by electrostatic gating. Techniques to control the twist angle between graphene layers have led to rapid experimental progress but improving sample quality is essential for separating the delicate correlated-electron physics from disorder effects. Owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to small doping inhomogeneity which can drastically modify the local potential landscape. This potential disorder is distinct from the twist-angle variation which has been studied elsewhere. Here, by using low temperature scanning tunneling spectroscopy and planar tunneling junction measurements, we demonstrate that flat bands in twisted bilayer graphene can amplify small doping inhomogeneity that surprisingly leads to carrier confinement, which in graphene could previously only be realized in the presence of a strong magnetic field.
Density perturbations at the decoupling epoch produce angular fluctuations in the temperature of the Cosmic Microwave Background (CMB) radiation that may appear as hot and cold spots. Observational data of the CMB includes instrumental noise in addition to the cosmological signal. One would like to determine which of the observed spots are produced by the noise and which correspond to signal. In this work we first present a statistical analysis of the first plus second year COBE/DMR map at 53 GHz that reveals the presence of cosmological signal in the data. The analysis is based on Harrison-Zeldovich Monte Carlo realizations and utilizes a generalized $\chi^2$ statistic. The method is applied to the number of spots and the fraction of the total area that appear above/below a certain value of the dispersion of the noise, including and excluding the quadrupole, giving $Q_{rms-PS}=15^{+3}_{-6}$, $18^{+5}_{-7} \mu K$ and $Q_{rms-PS}=18^{+3}_{-4}$, $21\pm6 \mu K$, at the $95\%$ confidence level, respectively. The data taken by the COBE/DMR experiment during the first two years at three different frequencies (31, 53 and 90 GHz) are used to determine which of the spots observed at 53 GHz appear simultaneously in the other two channels. The significance of those spots is determined by comparison of their area and signal-to-noise with noise Monte Carlo simulations. We point out two cold spots and one hot spot at positions $(l,b)\approx (-99^{\circ},57^{\circ}),(-21^{\circ},-45^{\circ}), (-81^{\circ},-33^{\circ})$ respectively, at the $95 \%$ confidence level.
The supernova remnant SN 1006 is a powerful source of high-energy particles and evolves in a relatively tenuous and uniform environment, though interacting with an atomic cloud in its northwestern limb. The X-ray image of SN 1006 reveals an indentation in the southwestern part of the shock front and the HI maps show an isolated cloud (southwestern cloud) having the same velocity as the northwestern cloud and whose morphology fits perfectly in the indentation. We performed spatially resolved spectral analysis of a set of small regions in the southwestern nonthermal limb and studied the deep X-ray spectra obtained within the XMM-Newton SN 1006 Large Program. We also analyzed archive HI data, obtained combining single dish and interferometric observations. We found that the best-fit value of the N_H derived from the X-ray spectra significantly increases in regions corresponding to the southwestern cloud, while the cutoff energy of the synchrotron emission decreases. The amount of the N_H variations corresponds perfectly with the HI column density of the southwestern cloud, as measured from the radio data. The decrease in the cutoff energy at the indentation clearly reveals that the back side of the cloud is actually interacting with the remnant. The southwestern limb therefore presents a unique combination of efficient particle acceleration and high ambient density, thus being the most promising region for gamma-ray hadronic emission in SN 1006. We estimate that such emission will be detectable with the Fermi telescope within a few years.
The zirconium isotopes with $A=$ 92$-$110 have one of the most complicated evolution of structure in the nuclear chart. In order to understand the structural evolution of these isotopes, we carry a detailed calculation in a definite symmetry-based framework, the interacting boson model with configuration mixing (IBM-CM). We compare our calculation to a large range of experimental data, such as energy levels, two neutron separation energies, $E2$ and $E0$ transition rates, isotope shifts and magnetic moments. The structural evolution of the low lying spectra of these isotopes is explained using the notion of intertwined quantum phase transitions (IQPTs), for which a QPT involving a crossing of two configurations (Type II) is accompanied by a QPT involving a shape evolution of each configuration separately (Type I). In our study, we find the occurrence of Type I QPT within the intruder configuration, changing from weakly deformed to prolate deformed and finally to $\gamma$-unstable, associated with the U(5), SU(3) and SO(6) dynamical symmetry limits of the IBM, respectively. Alongside the Type I QPT, we also find the occurrence of Type II QPT between the normal and intruder configurations, where both Types I and II have a critical-point near $A\approx100$. The good agreement of our calculation with the vast empirical data along the chain of isotopes demonstrates the relevance of IQPTs to the zirconium isotopes, and can serve as a case study to set path for new investigations of IQPTs in other nuclei and other physical systems.
In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process.
The feasibility for the alpha decay and the heavy particle decay from the even-even superheavy (SH) nuclei with Z = 116-124 have been studied within the Coulomb and proximity potential model (CPPM). The Universal formula for cluster decay (UNIV) of Poenaru et al., the Universal Decay Law (UDL) and the Scaling Law of Horoi et al., has also been used for the evaluation of the decay half lives. A comparison of our predicted half lives with the values evaluated using these empirical formulas are in agreement with each other and hence CPPM could be considered as a unified model for alpha and cluster decay studies. The spontaneous fission half lives of the corresponding parents have also been evaluated using the semi-empirical formula of Santhosh et al. Within our fission model, we have studied cluster formation probability for various clusters and the maximum cluster formation probability for the decay accompanying $^{298}$114 reveals its doubly magic behavior. In the plots for log_10(T_1/2) against the neutron number of the daughter in the corresponding decay, the half life is found to be the minimum for the decay leading to $^{298}$114 (Z = 114, N = 184) and this also indicate its doubly magic behavior. Most of the predicted half lives are well within the present upper limit for measurements and the computed alpha half lives for $^{290,292}$116 agrees well with the experimental data. We have thus confidently indicate towards a new island for the cluster radioactivity around the superheavy isotope $^{298}$114 and its neighbors and we hope to receive experimental information about the cluster decay half lives of these considered SHs, hoping to confirm the present calculations.
We introduce the idea of an n-simplex graph and games upon simplicial complexes. We then define moves on a labeled graph and pose the problem of whether given two labelings of a graph it is possible to change one into another via these moves. We then solve the problem for a given class of graphs. Once having found a solution for a given class of graphs we determine the number of different solutions that exist. We then use this to find an algorithm to determine whether a graph is (n+1)-colorable, and in particular, whether it is 3-colorable.
We present a millimetre molecular line survey of seven high mass loss rate carbon stars in both the northern and southern skies. A total of 196 emission lines (47 transitions) from 24 molecular species were detected. The observed CO emission is used to determine mass-loss rates and the physical structure of the circumstellar envelope, such as the density and temperature structure, using a detailed radiative transfer analysis. This enables abundances for the remaining molecular species to be determined. The derived abundances generally vary between the sources by no more than a factor of five indicating that circumstellar envelopes around carbon stars with high mass-loss rates have similar chemical compositions. However, there are some notable exceptions. The most striking difference between the abundances are reflecting the spread in the 12C/13C-ratio of about an order of magnitude between the sample stars, mainly reflecting the results of nucleosynthesis. The abundance of SiO also shows a variation of more than an order of magnitude between the sources and is on the average more than an order of magnitude more abundant than predicted from photospheric chemistry in thermal equilibrium. The over abundance of SiO is consistent with dynamical modelling of the stellar atmosphere and the inner parts of the wind where a pulsation-driven shock has passed. This scenario is possibly further substantiated by the relatively low amount of CS present in the envelopes. The chemistry occurring in the outer envelope is consistent with current photochemical models.
We present new determinations of the integrated H\alpha\ flux for ~1100 Galactic planetary nebulae measured from the Southern H-Alpha Sky Survey Atlas (SHASSA) and its northern counterpart, the Virginia Tech Spectral-Line Survey (VTSS). This catalogue is the largest homogeneous database of its kind, tripling the number of currently available measurements.
We started a program to construct several grids of suitable model atmospheres and synthetic spectra for hot subdwarf O stars computed, for comparative purposes, in LTE, NLTE, with and without metals. For the moment, we use our grids to perform fits on our spectrum of SDSS J160043.6+074802.9 (J1600+0748 for short), this unique pulsating sdO star. Our best fit is currently obtained with NLTE model atmospheres including carbon, nitrogen and oxygen in solar abundances, which leads to the following parameters for SDSS J1600+0748 : Teff = 69 060 +/- 2080 K, log g = 6.00 +/- 0.09 and log N(He)/N(H) = -0.61 +/- 0.06. Improvements are needed, however, particularly for fitting the available He II lines. It is hoped that the inclusion of Fe will help remedy the situation.
Grover's algorithm is one of the most famous algorithms which explicitly demonstrates how the quantum nature can be utilized to accelerate the searching process. In this work, Grover's quantum search problem is mapped to a time-optimal control problem. Resorting to Pontryagin's Minimum Principle we find that the time-optimal solution has the bang-singular-bang structure. This structure can be derived naturally, without integrating the differential equations, using the geometric control technique where Hamiltonians in the Schr\"odinger's equation are represented as vector fields. In view of optimal control, Grover's algorithm uses the bang-bang protocol to approximate the optimal protocol with a minimized number of bang-to-bang switchings to reduce the query complexity. Our work provides a concrete example how Pontryagin's Minimum Principle is connected to quantum computation, and offers insight into how a quantum algorithm can be designed.
RedGOLD searches for red-sequence galaxy overdensities while minimizing contamination from dusty star-forming galaxies. It imposes an NFW profile and calculates cluster detection significance and richness. We optimize these latter two parameters using both simulations and X-ray detected cluster catalogs, and obtain a catalog $\sim 80\%$ pure up to $z \sim 1$, and $\sim 100\%$ ($\sim 70\%$) complete at $z\le 0.6$ ( $z\lesssim1$) for galaxy clusters with $M \gtrsim 10^{14}\ {\rm M_{\odot}}$ at the CFHT-LS Wide depth. In the CFHT-LS W1, we detect 11 cluster candidates per $\rm deg^2$ out to $z\sim1.1$. When we optimize both completeness and purity, RedGOLD obtains a cluster catalog with higher completeness and purity than other public catalogs, obtained using CFHT-LS W1 observations, for $M \gtrsim 10^{14}\ {\rm M_{\odot}}$. We use X-ray detected cluster samples to extend the study of the X-ray temperature-optical richness relation to a lower mass threshold, and find a mass scatter at fixed richness of $\sigma_{lnM|\lambda}=0.39\pm0.07$ and $\sigma_{lnM|\lambda}=0.30\pm0.13$ for the Gozaliasl et al. (2014) and Mehrtens et al. (2012) samples. When considering similar mass ranges as previous work, we recover a smaller scatter in mass at fixed richness. We recover $93\%$ of the redMaPPer detections, and find that its richness estimates is on average $\sim 40-50\%$ larger than ours at $z>0.3$. RedGOLD recovers X-ray cluster spectroscopic redshifts at better than $5\%$ up to $z\sim1$, and the centers within a few tens of arcseconds.
We have carried out density functional theory based calculations of the size dependent formation energy and geometry of Pt islands on Ru(0001), to model Pt-Ru nanocatalysts which have been recently proposed as fuel cell anode. The Pt islands are found to prefer two-dimensional structures. Furthermore, a monotonic decrease in the formation energy per Pt atom suggests a propensity of Pt atoms to wet the Ru(0001) surface. Calculated energy barriers for the diffusion of Pt monomers and dimers on the facets and through the edges of a superstructure modeling a Ru nanoparticle indicate that these edges help reduce considerably the diffusion rates across them such that the Pt atoms prefer to remain in the facet on which they were adsorbed originally and form 2D islands.
In this updated and expanded version of our delayed Comment we show that the np backward cross section, as presented by the Uppsala group, is seriously flawed (more than 25 sd.). The main reason is the incorrect normalization of the data. We show also that their extrapolation method, used to determine the charged piNN coupling constant, is a factor of about 10 less accurate than claimed by Ericson et al. The large extrapolation error makes the determination of the coupling constant by the Uppsala group totally uninteresting.
Non-blazar Active Galactic Nuclei (AGN) have emerged as a new gamma-ray emitting source class on the extragalactic sky and started to deepen our understanding of the physical processes and the nature of AGN in general. The detection of Narrow Line Seyfert 1 galaxies in the Fermi-LAT energy regime, for example, offers important information for our understanding of jet formation and radio-loudness. Radio galaxies, on the other hand, have become particularly interesting at high (HE) and very high (VHE) gamma-ray energies. With their jets not directly pointing towards us (i.e. misaligned), they offer a unique tool to probe into the nature of the fundamental (and often hidden) physical processes in AGN. This review highlights and discusses some of the observational and theoretical progress achieved in the gamma-ray regime during recent years, including the evidence for unexpected spectral hardening in Centaurus A and extreme short-term variability as seen in IC 310 and M87.
We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a "determinant" map from this moduli surface to (Z/NZ)*; its fibers are the components of the surface. We define spaces of modular forms on these components and Hecke correspondences between them, and study how those spaces of modular forms behave as modules for the Hecke algebra. We discover that the component with determinant -1 is somehow the "dominant" one; we characterize the difference between its spaces of modular forms and the spaces of modular forms on the other components using forms with complex multiplication. Finally, we show some simplifications that arise when N is prime, including a complete determination of such CM-forms, and give numerical examples.
We show via the nonlinear semigroup theory in $L^1(\mathbb{R})$ that the $1$-D dynamic programming equation associated with a stochastic optimal control problem with multiplicative noise has a unique mild solution $\varphi\in C([0,T];W^{1,\infty}(\mathbb{R}))$ with $\varphi_{xx}\in C([0,T];L^1(\mathbb{R}))$. The $n$-dimensional case is also investigated.
We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable. We will refer to this as the factorization property of a selfdecomposable distribution; let L^f denote the set of all these distributions. The algebraic structure and various characterizations of L^f are studied. Some examples are discussed, the most interesting one being given by the Levy stochastic area integral. A nested family of subclasses L^f_n, n\ge 0, (or a filtration) of the class L^f is given.
Condensed Abstract: We present an extensive study of the inception of supernova explosions by following the evolution of the cores of two massive stars (15 Msun and 25 Msun) in two dimensions. Our calculations begin at the onset of core collapse and stop several 100 ms after the bounce, at which time successful explosions of the appropriate magnitude have been obtained. (...) Guided by our numerical results, we have developed a paradigm for the supernova explosion mechanism. We view a supernova as an open cycle thermodynamic engine in which a reservoir of low-entropy matter (the envelope) is thermally coupled and physically connected to a hot bath (the protoneutron star) by a neutrino flux, and by hydrodynamic instabilities. (...) In essence, a Carnot cycle is established in which convection allows out-of-equilibrium heat transfer mediated by neutrinos to drive low entropy matter to higher entropy and therefore extracts mechanical energy from the heat generated by gravitational collapse. We argue that supernova explosions are nearly guaranteed and self-regulated by the high efficiency of the thermodynamic engine. (...) Convection continues to accumulate energy exterior to the neutron star until a successful explosion has occurred. At this time, the envelope is expelled and therefore uncoupled from the heat source (the neutron star) and the energy input ceases. This paradigm does not invoke new or modified physics over previous treatments, but relies on compellingly straightforward thermodynamic arguments. It provides a robust and self-regulated explosion mechanism to power supernovae which is effective under a wide range of physical parameters.