ShantanuT01/DACTYL-Pretraining huggingface dataset:
We shall give a priori conditions on the illuminations $\phi_i$ such that the solutions to the Helmholtz equation $-div(a \nabla u^i)-k q u^i=0$ in \Omega, $u^i=\phi_i$ on $\partial\Omega$, and their gradients satisfy certain non-zero and linear independence properties inside the domain \Omega, provided that a finite number of frequencies k are chosen in a fixed range. These conditions are independent of the coefficients, in contrast to the illuminations classically constructed by means of complex geometric optics solutions. This theory finds applications in several hybrid problems, where unknown parameters have to be imaged from internal power density measurements. As an example, we discuss the microwave imaging by ultrasound deformation technique, for which we prove new reconstruction formulae.
Using the Spitzer IRAC camera we have obtained mid-IR photometry of the red giant branch stars in the Galactic globular cluster 47 Tuc. About 100 stars show an excess of mid-infrared light above that expected from their photospheric emission. This is plausibly due to dust formation in mass flowing from these stars. This mass loss extends down to the level of the horizontal branch and increases with luminosity. The mass loss is episodic, occurring in only a fraction of stars at a given luminosity. Using a simple model and our observations we derive mass loss rates for these stars. Finally, we obtain the first empirical mass loss formula calibrated with observations of Population II stars. The dependence on luminosity of our mass loss rate is considerably shallower than the widely used Reimers Law. The results presented here are the first from our Spitzer survey of a carefully chosen sample of 17 Galactic Globular Clusters, spanning the entire metallicity range from about one hundredth up to almost solar.
We present a first-principles theoretical study of electric field-and strain-controlled intrinsic half-metallic properties of zigzagged aluminium nitride (AlN) nanoribbons. We show that the half-metallic property of AlN ribbons can undergo a transition into fully-metallic or semiconducting behavior with application of an electric field or uniaxial strain. An external transverse electric field induces a full charge screening that renders the material semiconducting. In contrast, as uniaxial strain varies from compressive to tensile, a spin-resolved selective self-doping increases the half-metallic character of the ribbons. The relevant strain-induced changes in electronic properties arise from band structure modifications at the Fermi level as a consequence of a spin-polarized charge transfer between pi-orbitals of the N and Al edge atoms in a spin-resolved self-doping process. This band structure tunability indicates the possibility ofdesigning magnetic nanoribbons with tunable electronic structure by deriving edge states from elements with sufficiently different localization properties. Finite temperature molecular dynamics reveal a thermally stable half-metallic nanoribbon up to room temperature.
We study the average X-ray and soft gamma-ray spectrum of Cyg X-1 in the hard spectral state, using data from INTEGRAL. We compare these results with those from CGRO, and find a good agreement. Confirming previous studies, we find the presence of a high-energy MeV tail beyond a thermal-Comptonization spectrum; however, the tail is much softer and weaker than that recently published by Laurent et al. In spite of this difference, the observed high-energy tail could still be due to the synchrotron emission of the jet of Cyg X-1, as claimed by Laurent et al.   To test this possibility, we study optically-thin synchrotron and self-Compton emission from partially self-absorbed jets. We develop formalisms for calculating both emission of the jet base (which we define here as the region where the jet starts its emission) and emission of the entire jet. We require the emission to match that observed at the turnover energy. The optically thin emission is dominated by that from the jet base, and it has to become self-absorbed within it at the turnover frequency. We find this implies the magnetic field strength at the jet base of B_0 prop. to z_0^4, where z_0 is the distance of the base from the black-hole centre. The value of B_0 is then constrained from below by the condition that the self-Compton emission is below an upper limit in the GeV range, and from above by the condition that the Poynting flux does not exceed the jet kinetic power. This yields B_0 of the order of ~10^4 G and the location of the jet base at ~10^3 gravitational radii. Using our formalism, we find the MeV tail can be due to jet synchrotron emission, but this requires the electron acceleration at a rather hard power-law index, p~1.3-1.6. For acceleration indices of p> 2, the amplitude of the synchrotron component is much below that of MeV tail, and its origin is likely to be due to hybrid Comptonization in the accretion flow.
Generic inhomogeneous steady states in an asymmetric exclusion process on a ring with a pair of point bottlenecks are studied. We show that, due to an underlying universal feature, measurements of coarse-grained steady-state densities in this model resolve the bottleneck structures only partially. Unexpectedly, it displays localization-delocalization transitions and confinement of delocalized domain walls, controlled by the interplay between particle number conservation and bottleneck competition for moderate particle densities.
Multipartite quantum correlations are important resources for the development of quantum information and computation protocols. However, the resourcefulness of multipartite quantum correlations in practical settings is limited by its fragility under decoherence due to environmental interactions. Though there exist protocols to protect bipartite entanglement under decoherence, the implementation of such protocols for multipartite quantum correlations has not been sufficiently explored. Here, we study the effect of local amplitude damping channel on the generalized Greenberger-Horne-Zeilinger state, and use a protocol of optimal reversal quantum weak measurement to protect the multipartite quantum correlations. We observe that the weak measurement reversal protocol enhances the robustness of multipartite quantum correlations. Further it increases the critical damping value that corresponds to entanglement sudden death. To emphasize the efficacy of the technique in protection of multipartite quantum correlation, we investigate two proximately related quantum communication tasks, namely, quantum teleportation in a one sender, many receivers setting and multiparty quantum information splitting, through a local amplitude damping channel. We observe an increase in the average fidelity of both the quantum communication tasks under the weak measurement reversal protocol. The method may prove beneficial, for combating external interactions, in other quantum information tasks using multipartite resources.
Cylindrically symmetric inhomogeneous string cosmological models are investigated in presence of string fluid as a source of matter. To get the three types of exact solutions of Einstein's field equations we assume $A = f(x)k(t)$, $B = g(x)\ell(t)$ and $C = h(x)\ell(t)$. Some physical and geometric aspects of the models are discussed.
In peripheral collisions of relativistic heavy ions highly excited spectators containing Lambda-hyperons can be produced. Such strange spectator matter may undergo a break-up into many fragments (multifragmentation) as it is well established for ordinary nuclear systems. We generalize the statistical multifragmentation model, previously successfully used for the description of experimental data, for the case of hypernuclear systems. We predict relative yields of hypernuclei and the main characteristics of such a break-up. We point at a connection of this phenomenon with a liquid-gas phase transition in hypermatter.
The collapse and fragmentation of initially prolate and oblate, magnetic molecular clouds is calculated in three dimensions with a gravitational, radiative hydrodynamics code. The code includes magnetic field effects in an approximate manner: magnetic pressure, tension, braking, and ambipolar diffusion are all modelled. The parameters varied for both the initially prolate and oblate clouds are the initial degree of central concentration of the radial density profile, the initial angular velocity, and the efficiency of magnetic braking (represented by a factor $f_{mb} = 10^{-4}$ or $10^{-3}$). The oblate cores all collapse to form rings that might be susceptible to fragmentation into multiple systems. The outcome of the collapse of the prolate cores depends strongly on the initial density profile. Prolate cores with central densities 20 times higher than their boundary densities collapse and fragment into binary or quadruple systems, whereas cores with central densities 100 times higher collapse to form single protostars embedded in bars. The inclusion of magnetic braking is able to stifle protostellar fragmentation in the latter set of models, as when identical models were calculated without magnetic braking (Boss 2002), those cores fragmented into binary protostars. These models demonstrate the importance of including magnetic fields in studies of protostellar collapse and fragmentation, and suggest that even when magnetic fields are included, fragmentation into binary and multiple systems remains as a possible outcome of protostellar collapse.
In this paper, we define the $4$-girth-thickness $\theta(4,G)$ of a graph $G$ as the minimum number of planar subgraphs of girth at least $4$ whose union is $G$. We obtain the $4$-girth-thickness of the arbitrary complete graph $K_n$ getting that $\theta(4,K_n)=\left\lceil \frac{n+2}{4}\right\rceil$ for $n\not=6,10$ and $\theta(4,K_6)=3$.
We review the search for the quark-gluon plasma using the signal of the suppression of J/psi production in high-energy heavy-ion collisions. Recent observations of anomalous J/psi suppression in high-energy Pb-Pb collisions observed by the NA50 Collaboration are examined and compared with earlier results from pA and nucleus-nucleus collisions with heavy ions of smaller mass numbers. The anomalous suppression of J/psi production in Pb-Pb collisions can be explained as due to the occurrence of a new phase of strong J/psi absorption, which sets in when the number of nucleon-nucleon collisions at a spatial point exceeds about 4 and corresponds to a local energy density of about 3.4 GeV/fm**3.
We study the Calabi-Yau phase of a certain class of (0,2) models. These are conjectured to be equivalent to exact (0,2) superconformal field theories which have been constructed recently. Using the methods of toric geometry we discuss in a few examples the problem of resolving the singularities of such models and calculate the Euler characteristic of the corresponding gauge bundles.
We study the quantum dynamics of a one-dimensional gas of impenetrable bosons on a ring, and investigate the interference that results when an initially trapped gas localized on one side of the ring is released, split via an optical-dipole grating, and recombined on the other side of the ring. Large visibility interference fringes arise when the wavevector of the optical dipole grating is larger than the effective Fermi wavevector of the initial gas.
In this letter, we report on successful electrical spin injection and detection in \textit{n}-type germanium-on-insulator (GOI) using a Co/Py/Al$_{2}$O$_{3}$ spin injector and 3-terminal non-local measurements. We observe an enhanced spin accumulation signal of the order of 1 meV consistent with the sequential tunneling process via interface states in the vicinity of the Al$_{2}$O$_{3}$/Ge interface. This spin signal is further observable up to 220 K. Moreover, the presence of a strong \textit{inverted} Hanle effect points at the influence of random fields arising from interface roughness on the injected spins.
Solvation of small and large clusters are studied by simulation, considering a range of solvent-solute attractive energy strengths. Over a wide range of conditions, both for solvation in the Lennard-Jones liquid and in the SPC model of water, it is shown that the mean solvent density varies linearly with changes in solvent-solute adhesion or attractive energy strength. This behavior is understood from the perspective of Weeks' theory of solvation [Ann. Rev. Phys. Chem. 2002, 53, 533] and supports theories based upon that perspective.
We investigate the solution of the continued fraction equation by which we determine "the renormalized angular momentum parameter", $\nu$, in the formalism developed by Leaver and Mano, Suzuki, and Takasugi. In this formalism, we describe the homogeneous solutions of the radial Teukolsky equation, which is the basic equation of the black hole perturbation formalism. We find that, contrary to the assumption made in previous works, the solution, $\nu$, becomes complex valued as $\omega$ (the angular frequency) becomes large for each $l$ and $m$ (the degree and order of the spin-weighted spheroidal harmonics). We compare the power radiated by gravitational waves from a particle in a circular orbit in the equatorial plane around a Kerr black hole in two ways, one using the Mano-Suzuki-Takasugi formalism with complex $\nu$ and the other using a direct numerical integration method. We find that the two methods produce consistent results. These facts prove the validity of using complex solutions to determine the homogeneous solutions of the Teukolsky equation.
We calculate the cross section and the beam asymmetry for exclusive photoproduction of charmed particles near threshold ($\gamma+p\to \Lambda_c^+ +\bar{D^0}$), in the framework of an effective Lagrangian model. We discuss the sensitivity of these observables to the magnetic moment of the $\Lambda_c$ baryon and of the coupling constant in the $p\Lambda_c D$ vertex. We show that exclusive measurements allow, in principle, to determine the magnetic moments of charmed baryons.
Let $E/F$ be a cyclic Galois extension of degree $p^l$ with Galois group $G$. It is shown that the Galois module structure of both sides of the Kummer pairing (for Kummer extensions of $E$) are the same. In other words, we show that the Kummer duality holds in the level of finitely generated $G$-modules.
This work concerns the Ornstein-Uhlenbeck type process associated to a positive self-similar Markov process $(X(t))_{t\geq 0}$ which drifts to $\infty$, namely $U(t):= {\rm e}^{-t}X({\rm e}^t-1)$. We point out that $U$ is always a (topologically) recurrent Markov process and identify its invariant measure in terms of the law of the exponential functional $\hat I := \int_0^\infty \exp(\hat\xi_s) {\rm d}s$, where $\hat\xi$ is the dual of the real-valued L\'evy process $\xi$ related to $X$ by the Lamperti transformation. This invariant measure is infinite (i.e. $U$ is null-recurrent) if and only if $\xi_1\not \in L^1(\mathbb{P})$. In that case, we determine the family of L\'evy processes $\xi$ for which $U$ fulfills the conclusions of the Darling-Kac theorem. Our approach relies crucially on another generalized Ornstein-Uhlenbeck process that can be associated to the L\'evy process $\xi$, namely $V(t) := \exp(\xi_t)\left(\int_0^t \exp(-\xi_s){\rm d}s +V(0)\right)$, and properties of time-substitutions based on additive functionals.
Horndeski gravity is the most general scalar tensor theory, with a single scalar field, leading to second order field equations and after the GW170817 it has been severely constrained. In this paper, we study the analogue of Horndeski's theory in the teleparallel gravity framework were gravity is mediated through torsion instead of curvature. We show that, even though, many terms are the same as in the curvature case, we have much richer phenomenology in the teleparallel setting because of the nature of the torsion tensor. Moreover, Teleparallel Horndenski contains the standard Horndenski gravity as a subcase and also contains many modified Teleparallel theories considered in the past, such as $f(T)$ gravity or Teleparallel Dark energy. Thus, due to the appearing of a new term in the Lagrangian, this theory can explain dark energy without a cosmological constant, may describe a crossing of the phantom barrier, explain inflation and also solve the tension for $H_0$, making it a good candidate for a correct modified theory of gravity.
We report studies of the response of a massless particle confined by a potential. At large momentum transfer q it exhibits \tilde{y} or equivalently Nachtmann \xi scaling, and acquires a constant width independent of q. This width has a contribution from the final state interactions of the struck particle, which persists in the q->\infty limit. The width of the response predicted using plane wave impulse approximation is smaller because of the neglect of final state interactions in that approximation. However, the exact response may be obtained by folding the approximate response with a function representing final state interaction effects. We also study the response obtained from the momentum distribution assuming that the particle is on the energy shell both before and after being struck. Quantitative results are presented for the special case of a linear confining potential. In this case the response predicted with the on-shell approximation has correct values for the total strength, mean energy and width, however its shape is wrong.
Equi-Energy Sampling (EES, for short) is a method to speed up the convergence of the Metropolis chain, when the latter is slow. We show that there are still models like the mean-field Potts model, where EES does not converge rapidly in certain temperature regimes. Indeed we will show that EES is slowly mixing on the mean-field Potts model, in a regime below the critical temperature. Though we will concentrate on the Potts model with three colors, our arguments remain valid for any number of colors $q \ge 3$, if we adapt the temperature regime. For the situation of the mean-field Potts model this answers a question posed in \cite{HuaKou}.
In image classification task, feature extraction is always a big issue. Intra-class variability increases the difficulty in designing the extractors. Furthermore, hand-crafted feature extractor cannot simply adapt new situation. Recently, deep learning has drawn lots of attention on automatically learning features from data. In this study, we proposed multi-subspace neural network (MSNN) which integrates key components of the convolutional neural network (CNN), receptive field, with subspace concept. Associating subspace with the deep network is a novel designing, providing various viewpoints of data. Basis vectors, trained by adaptive subspace self-organization map (ASSOM) span the subspace, serve as a transfer function to access axial components and define the receptive field to extract basic patterns of data without distorting the topology in the visual task. Moreover, the multiple-subspace strategy is implemented as parallel blocks to adapt real-world data and contribute various interpretations of data hoping to be more robust dealing with intra-class variability issues. To this end, handwritten digit and object image datasets (i.e., MNIST and COIL-20) for classification are employed to validate the proposed MSNN architecture. Experimental results show MSNN is competitive to other state-of-the-art approaches.
We study the quantum-mechanical decay of a Schwarzschild-like black hole into almost-flat space and weak radiation at a very late time, evaluating quantum amplitudes (not just probabilities) for transitions from initial to final states. No information is lost. The model contains gravity and a massless scalar field. The quantum amplitude to go from given initial to final bosonic data in a slightly complexified time-interval $T={\tau}{\exp}(-i{\theta})$ at infinity is approximately $\exp(-I)$, where $I$ is the (complex) Euclidean action of the classical solution filling in between the boundary data. And in a locally supersymmetric (supergravity) theory, the amplitude const. exp(-I) is exact. Dirichlet boundary data for gravity and the scalar field are posed on an initial spacelike hypersurface extending to spatial infinity, just prior to collapse, and on a corresponding final spacelike surface, sufficiently far to the future of the initial surface to catch all the Hawking radiation. In an averaged sense this radiation has an approximately spherically-symmetric distribution. If the time-interval $T$ were exactly real, the resulting `hyperbolic Dirichlet boundary-value problem' would not be well posed. If instead (`Euclidean strategy'), one takes $T$ complex, as above ($0<\theta{\leq}{\pi}/2$), the field equations become strongly elliptic, with a unique solution to the classical boundary-value problem. Expanding the bosonic part of the action to quadratic order in perturbations about the classical solution gives the quantum amplitude for weak-field final configurations, up to normalization. Such amplitudes are calculated for weak final scalar fields.
The uncertainty relation for continuous variables due to Byalinicki-Birula and Mycielski expresses the complementarity between two $n$-uples of canonically conjugate variables $(x_1,x_2,\cdots x_n)$ and $(p_1,p_2,\cdots p_n)$ in terms of Shannon differential entropy. Here, we consider the generalization to variables that are not canonically conjugate and derive an entropic uncertainty relation expressing the balance between any two $n$-variable Gaussian projective measurements. The bound on entropies is expressed in terms of the determinant of a matrix of commutators between the measured variables. This uncertainty relation also captures the complementarity between any two incompatible linear canonical transforms, the bound being written in terms of the corresponding symplectic matrices in phase space. Finally, we extend this uncertainty relation to R\'enyi entropies and also prove a covariance-based uncertainty relation which generalizes Robertson relation.
An explicit Dirichlet series is obtained, which represents an analytic function of $s$ in the half-plane $\Re s>1/2$ except for having simple poles at points $s_j$ that correspond to exceptional eigenvalues $\lambda_j$ of the non-Euclidean Laplacian for Hecke congruence subgroups $\Gamma_0(N)$ by the relation $\lambda_j=s_j(1-s_j)$ for $j=1,2,..., S$. Coefficients of the Dirichlet series involve all class numbers $h_d$ of real quadratic number fields. But, only the terms with $h_d\gg d^{1/2-\epsilon}$ for sufficiently large discriminants $d$ contribute to the residues $m_j/2$ of the Dirichlet series at the poles $s_j$, where $m_j$ is the multiplicity of the eigenvalue $\lambda_j$ for $j=1,2,..., S$. This may indicate (I'm not able to prove yet) that the multiplicity of exceptional eigenvalues can be arbitrarily large. On the other hand, by density theorem [3] the multiplicity of exceptional eigenvalues is bounded above by a constant depending only on $N$.