ShantanuT01/DACTYL-Pretraining huggingface dataset:
Twisting by a G-torsor an object endowed with an action of a group G is a classical tool. For instance one finds in the paragraph 5.3 of the book "cohomologie galoisienne" by Serre, the description of the "op\'eration de torsion" in a particular context. The aim of this note is to give a formalization of this twisting operation as general as possible in the algebraic geometric framework and to present a few applications. We will focus in particular to the application to the problem of specialization of covers addressed by P. D\`ebes and al. in a series of papers.
The calculations of three-body direct nuclear reactions with nonlocal optical potentials are performed for the first time using the framework of Faddeev-type scattering equations. Important nonlocality effect is found for transfer reactions like d+16O -> p + 17O often improving the description of the experimental data.
The mixed-spin Ising model on a decorated square lattice with two different decorating spins of the integer magnitudes S_B = 1 and S_C = 2 placed on horizontal and vertical bonds of the lattice, respectively, is examined within an exact analytical approach based on the generalized decoration-iteration mapping transformation. Besides the ground-state analysis, finite-temperature properties of the system are also investigated in detail. The most interesting numerical result to emerge from our study relates to a striking critical behaviour of the spontaneously ordered 'quasi-1D' spin system. It was found that this quite remarkable spontaneous order arises when one sub-lattice of the decorating spins (either S_B or S_C) tends towards their 'non-magnetic' spin state S = 0 and the system becomes disordered only upon further single-ion anisotropy strengthening. The effect of single-ion anisotropy upon the temperature dependence of the total and sub-lattice magnetization is also particularly investigated.
Most theoretical descriptions of the production of solar flare bremsstrahlung radiation assume the collision of dilute accelerated particles with a cold, dense target plasma, neglecting interactions of the fast particles with each other. This is inadequate for situations where collisions with this background plasma are not completely dominant, as may be the case in, for example, low-density coronal sources. We aim to formulate a model of a self-interacting, entirely fast electron population in the absence of a dense background plasma, to investigate its implications for observed bremsstrahlung spectra and the flare energy budget. We derive approximate expressions for the time-dependent distribution function of the fast electrons using a Fokker-Planck approach. We use these expressions to generate synthetic bremsstrahlung X-ray spectra as would be seen from a corresponding coronal source. We find that our model qualitatively reproduces the observed behaviour of some flares. As the flare progresses, the model's initial power-law spectrum is joined by a lower energy, thermal component. The power-law component diminishes, and the growing thermal component proceeds to dominate the total emission over timescales consistent with flare observations. The power-law exhibits progressive spectral hardening, as is seen in some flare coronal sources. We also find that our model requires a factor of 7 - 10 fewer accelerated electrons than the cold, thick target model to generate an equivalent hard X-ray flux. This model forms the basis of a treatment of self-interactions among flare fast electrons, a process which affords a more efficient means to produce bremsstrahlung photons and so may reduce the efficiency requirements placed on the particle acceleration mechanism. It also provides a useful description of the thermalisation of fast electrons in coronal sources.
We present high-resolution Keck optical spectra of the very young substellar eclipsing binary 2MASS J05352184-0546085, obtained during eclipse of the lower-mass (secondary) brown dwarf. The observations yield the spectrum of the higher-mass (primary) brown dwarf alone, with negligible (~1.6%) contamination by the secondary. We perform a simultaneous fine-analysis of the TiO-epsilon band and the red lobe of the KI doublet, using state-of-the-art PHOENIX Dusty and Cond synthetic spectra. Comparing the effective temperature and surface gravity derived from these fits to the {\it empirically} determined surface gravity of the primary (logg=3.5) then allows us to test the model spectra as well as probe the prevailing photospheric conditions. We find that: (1) fits to TiO-epsilon alone imply Teff=2500 \pm 50K; (2) at this Teff, fits to KI imply logg=3.0, 0.5 dex lower than the true value; and (3) at the true logg, KI fits yield Teff=2650 \pm 50K, ~150K higher than from TiO-epsilon alone. On the one hand, these are the trends expected in the presence of cool spots covering a large fraction of the primary's surface (as theorized previously to explain the observed Teff reversal between the primary and secondary). Specifically, our results can be reproduced by an unspotted stellar photosphere with Teff=2700K and (empirical) logg=3.5, coupled with axisymmetric cool spots that are 15% cooler (2300K), have an effective logg=3.0 (0.5 dex lower than photospheric), and cover 70% of the surface. On the other hand, the trends in our analysis can also be reproduced by model opacity errors: there are lacks in the synthetic TiO-epsilon opacities, at least for higher-gravity field dwarfs. Stringently discriminating between the two possibilities requires combining the present results with an equivalent analysis of the secondary (predicted to be relatively unspotted compared to the primary).
We investigate the properties of an antikaon in medium, regarding itas a MIT bag. We first construct the MIT bag model for a kaon with$\sigma^*$ and $\phi$ in order to describe the interaction of$s$-quarks in hyperonic matter in the framework of the modifiedquark-meson coupling model. The coupling constant $g'^{B_K}_\sigma$in the density-dependent bag constant $B(\sigma)$ is treated as afree parameter to reproduce the optical potential of a kaon in asymmetric matter and all other couplings are determined by usingSU(6) symmetry and the quark counting rule. With various values ofthe kaon potential, we calculate the effective mass of a kaon inmedium to compare it with that of a point-like kaon. We thencalculate the population of octet baryons, leptons and $K^-$ and theequation of state for neutron star matter. The results show thatkaon condensation in hyperonic matter is sensitive to the $s$-quarkinteraction and also to the way of treating the kaon. The mass andthe radius of a neutron star are obtained by solving theTolmann-Oppenheimer-Volkoff equation.
We consider the influence of a spin accumulation in a normal metal on the magnetic statics and dynamics in an adjacent magnetic insulator. In particular, we focus on arbitary angles between the spin accumulation and the easy-axis of the magnetic insulator. Based on Landau-Lifshitz-Gilbert phenomenology supplemented with magnetoelectronic circuit theory, we find that the magnetic texture twists into a stable configuration that turns out to be described by a virtual, or image, domain wall configuration, i.e., a domain wall outside the ferromagnet. We show that even when the spin accumulation is perpendicular to the anisotropy axis, the magnetic texture develops a component parallel to the spin accumulation for sufficiently large spin bias. The emergence of this parallel component gives rise to threshold behavior in the spin Hall magnetoresistance and nonlocal magnon transport. This threshold can be used to design novel spintronic and magnonic devices that can be operated without external magnetic fields.
In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a comparison principle. We then illustrate our abstract statements for different concrete examples, where new results are achieved. In a preliminary step, we prove some well-posedness results for some nonlinear and nonautonomous evolution equations.
I argue that the large scale departure from axisymmetry of the Eta Carinae nebula can be explained by the binary stars model of Eta Carinae. The companion diverts the wind blown by the primary star, by accreting from the wind and possibly by blowing its own collimated fast wind (CFW). The effect of these processes depends on the orbital separation, hence on the orbital phase of the eccentric orbit. The variation of the mass outflow from the binary system with the orbital phase leads to a large-scale departure from axisymmetry along the equatorial plane, as is observed in Eta Car. I further speculated that such a companion may have accreted a large fraction of the mass that was expelled in the Great Eruption of 1850 and the Lesser Eruption of 1890. The accretion process was likely to form an accretion disk, with the formation of a CFW, or jets, on the two sides of the accretion disk. The CFW may have played a crucial role in the formation of the two lobes.
We present a class of models in the framework of gauge mediation supersymmetry breaking where the standard model is supplemented by additional U(1) symmetry which acts only on the third generation fermions. The messenger fields carry non-trivial U(1) charge and are vector-like particles under this symmetry. This leads to additional contribution to the soft supersymmetry breaking mass terms for the third generation squarks and sleptons. In this framework we show that the muon g-2 anomaly, the observed 125 GeV Higgs boson mass and the detected relic dark matter abundance (gravitino in our case) can be simultaneously accommodated. The resolution of the muon g-2 anomaly, in particular, yields the result that the first two generation squark masses, as well the gluino mass, should be <~ 2.5 TeV, which will be tested at LHC14.
The truncation formulae of $D=11$ supergravity on $S^7$ to $D=4$ ${\cal N} =8$ SO(8)-gauged supergravity are completed to include the full non-linear dependence of the $D=11$ three-form potential $\hat A_{(3)}$ on the $D=4$ fields, and their consistency is shown. The full embedding into $\hat A_{(3)}$ is naturally expressed in terms of a restricted version, still ${\cal N} =8$ but only SL(8)--covariant, of the $D=4$ tensor hierarchy. The redundancies introduced by this approach are removed at the level of the field strength $\hat F_{(4)}$ by exploiting $D=4$ duality relations. Finally, new expressions for the full consistent truncation formulae are given that are, for the first time, explicit in all $D=4$ fields.
It is well-known that the triangulations of the disc with $n+2$ vertices on its boundary are counted by the $n$th Catalan number $C(n)=\frac{1}{n+1}{2n \choose n}$. This paper deals with the generalisation of this problem to any arbitrary compact surface $S$ with boundaries. We obtain the asymptotic number of simplicial decompositions of the surface $S$ with $n$ vertices on its boundary. More generally, we determine the asymptotic number of dissections of $S$ when the faces are $\delta$-gons with $\delta$ belonging to a set of admissible degrees $\Delta\subseteq \{3,4,5,...\}$. We also give the limit laws of certain parameters of such dissections.
We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two non-interacting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.
Magnons are the elementary excitations of the magnetic order that carry spin, momentum, and energy. Here we compare the magnon with the ferron, i.e. the elementary excitation of the electric dipolar order that transports polarization and heat in ferroelectrics.
This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an $L^2$ maximum principle for the fluid interface. We also show global in time existence for strong and weak solutions with initial data controlled by explicit constants. Furthermore we refine the estimates from our paper \cite{PDPB} to obtain global existence and uniqueness for strong solutions with larger initial data than we previously had in 2D. Finally we provide global in time results in critical spaces, giving solutions with bounded slope and time integrable bounded curvature.
We study the Das-Jevicki collective field description of arbitrary classical solutions in the c=1 matrix model, which are believed to describe nontrivial spacetime backgrounds in 2d string theory. Our analysis naturally includes the case of a Fermi droplet cosmology: a finite size droplet of Fermi fluid, made up of a finite number of eigenvalues. We analyze properties of the coordinates in which the metric in the collective field theory is trivial, and comment on the form of the interaction terms in these coordinates.
In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results apply also to the traps having a small quadratic anharmonicity. We show the errors introduced when a Gaussian potential is approximated with a parabolic potential, these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies of the collective excitations in shallow spherically symmetric and 1D traps.
Bright small-scale magnetic elements found mainly in intergranular lanes at the solar surface are named bright points (BPs). They show high contrasts in Fraunhofer G-band observations and are described by nearly vertical slender flux tubes or sheets. A recent comparison between BP observations in the ultraviolet (UV) and visible spectral range recorded with the balloon-borne observatory SUNRISE and state-of-the-art magnetohydrodynamical (MHD) simulations revealed a kiloGauss magnetic field for 98% of the synthetic BPs. Here we address the opposite question, namely which fraction of pixels hosting kiloGauss fields coincides with an enhanced G-band brightness. We carried out 3D radiation MHD simulations for three magnetic activity levels (corresponding to the quiet Sun, weak and strong plage) and performed a full spectral line synthesis in the G-band. Only 7% of the kiloGauss pixels in our quiet-Sun simulation coincide with a brightness lower than the mean quiet-Sun intensity, while 23% of the pixels in the weak-plage simulation and even 49% in the strong-plage simulation are associated with a local darkening. Dark strong-field regions are preferentially found in the cores of larger flux patches that are rare in the quiet Sun, but more common in plage regions, often in the vertices of granulation cells. The significant brightness shortfall in the core of larger flux patches coincide with a slight magnetic field weakening. KiloGauss elements in the quiet Sun are on average brighter than similar features in plage regions. Almost all strong-field pixels display a more or less vertical magnetic field orientation. Hence in the quiet Sun, G-band BPs correspond almost one-to-one with kiloGauss elements. In weak plage the correspondence is still very good, but not perfect.
The nuclear collective response at finite temperature is investigated for the first time in the quantum framework of the small amplitude limit of the extended TDHF approach, including a non-Markovian collision term. It is shown that the collision width satisfies a secular equation. By employing a Skyrme force, the isoscalar monopole, isovector dipole and isoscalar quadrupole excitations in $^{40}Ca$ are calculated and important quantum features are pointed out. The collisional damping due to decay into incoherent 2p-2h states is small at low temperatures but increases rapidly at higher temperatures.
New information has recently become available on the fundamental plane for various samples of early-type galaxies with redshift up to 1.3, both in clusters and in the field. This information is reviewed and clues are derived on the evolution of spheroids over the last two thirds of the Universe lifetime as a function of galaxy mass and environment, in comparison with the predictions of the hierarchical models of galaxy formation. Using the Universe as a time-machine and interpreting changes in M/L ratio as age differences, we see that the age increases with galaxy mass in all environments, cluster galaxies with any mass are older than field galaxies with the same mass, and the age difference between cluster and field galaxies increases with mass. The first two results confirm those obtained with other methods, and are reproduced by the most recent incarnation of the hierarchical models, while the third result is new and appears in contrast with the predictions of these models.
We use quantum optimal control to identify fast collision-based two-qubit $\sqrt{\text{SWAP}}$ gates in ultracold atoms. We show that a significant speed up can be achieved by optimizing the full gate instead of separately optimizing the merge-wait-separate sequence of the trapping potentials. Our optimal strategy does not rely on the atoms populating the lowest eigenstates of the merged potential, and it crucially includes accumulation of quantum phases before the potentials are fully merged. Our analyses transcend the particular trapping geometry, but to compare with previous works, we present systematic results for an optical lattice and find greatly improved gate durations and fidelities.
We investigate whether the late-time (at $z\leq 100$) velocity dispersion expected in Warm Dark Matter scenarios could have some effect on the cosmic web (i.e., outside of virialized halos). We consider effective hydrodynamical equations, with a pressurelike term that agrees at the linear level with the analysis of the Vlasov equation. Then, using analytical methods, based on perturbative expansions and the spherical dynamics, we investigate the impact of this term for a 1 keV dark matter particle. We find that the late-time velocity dispersion has a negligible effect on the power spectrum on perturbative scales and on the halo mass function. However, it has a significant impact on the probability distribution function of the density contrast at $z \sim 3$ on scales smaller than $0.1 h^{-1}$Mpc, which correspond to Lyman-$\alpha$ clouds. Finally, we note that numerical simulations should start at $z_i\geq 100$ rather than $z_i \leq 50$ to avoid underestimating gravitational clustering at low redshifts.
A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann--Robertson--Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.
The competition among reaction processes of a weakly-bound projectile at intermediate times of a slow collision has been unraveled. This has been done using a two-center molecular continuum within a semiclassical, time-dependent coupled-channel reaction model. Dynamical probabilities of elastic scattering, transfer and breakup agree with those derived from the direct integration of the time-dependent Schr\"odinger equation, demonstrating the usefulness of a two-center molecular continuum for gaining insights into the reaction dynamics of exotic nuclei.
We present spectral analysis of five NuSTAR and Swift observations of GX 339-4 taken during a failed outburst in summer 2013. These observations cover Eddington luminosity fractions in the range ~0.9-6%. Throughout this outburst, GX 339-4 stayed in the hard state, and all five observations show similar X-ray spectra with a hard power-law with a photon index near 1.6 and significant contribution from reflection. Using simple reflection models we find unrealistically high iron abundances. Allowing for different photon indices for the continuum incident on the reflector relative to the underlying observed continuum results in a statistically better fit and reduced iron abundances. With a photon index around 1.3, the input power-law on the reflector is significantly harder than that which is directly observed. We study the influence of different emissivity profiles and geometries and consistently find an improvement when using separate photon indices. The inferred inner accretion disk radius is strongly model dependent, but we do not find evidence for a truncation radius larger than 100 r_g in any model. The data do not allow independent spin constraints but the results are consistent with the literature (i.e., a>0). Our best-fit models indicate an inclination angle in the range 40-60 degrees, consistent with limits on the orbital inclination but higher than reported in the literature using standard reflection models. The iron line around 6.4 keV is clearly broadened, and we detect a superimposed narrow core as well. This core originates from a fluorescence region outside the influence of the strong gravity of the black hole and we discuss possible geometries.
We consider a family of weights which permit to generalize the Leray procedure to obtain weak suitable solutions of the 3D incom-pressible Navier-Stokes equations with initial data in weighted L 2 spaces. Our principal result concerns the existence of regular global solutions when the initial velocity is an axisymmetric vector field without swirl such that both the initial velocity and its vorticity belong to L 2 ((1 + r 2) -- $\gamma$ 2 dx), with r = x 2 1 + x 2 2 and $\gamma$ $\in$ (0, 2).
Enumeration of various types of lattice polygons and in particular polyominoes is of primary importance in many machine learning, pattern recognition, and geometric analysis problems. In this work, we develop a large deviation principle for convex polyominoes under different restrictions, such as fixed area and/or perimeter.
To describe the nonequilibrium states of the system, a new thermodynamic parameter - system lifetime - is introduced. Statistical distributions that describe the behavior of energy and lifetime are recorded. Entropy and obtained thermodynamic relations are compared with the results of Extended Irreversible thermodynamics, where as an additional parameter selected fluxes. For the case of thermal conductivity explicit expressions are obtained for average lifetime and conjugate thermodynamic quantity. It is shown that near the equilibrium state, when is only one stationary nonequilibrium state, flows can only reduce the average system lifetime. But there are possibilities to increase the average lifetime of the system.