ShantanuT01/DACTYL-Pretraining huggingface dataset:
This article is concerned with the existence of nonnegative weak solutions to a particular fourth-order partial differential equation: it is a formal gradient flow with respect to a generalized Wasserstein transportation distance with nonlinear mobility. The corresponding free energy functional is referred to as generalized Fisher information functional since it is obtained by autodissipation of another energy functional which generates the heat flow as its gradient flow with respect to the aforementioned distance. Our main results are twofold: For mobility functions satisfying a certain regularity condition, we show the existence of weak solutions by construction with the well-known minimizing movement scheme for gradient flows. Furthermore, we extend these results to a more general class of mobility functions: a weak solution can be obtained by approximation with weak solutions of the problem with regularized mobility.
We show that the intriguing observation of noise enhancement in the charge transport through two vertically coupled quantum dots can be explained by the interplay of quantum coherence and strong Coulomb blockade. We demonstrate that this novel mechanism for super-Poissonian charge transfer is very sensitive to decoherence caused by electron-phonon scattering as inferred from the measured temperature dependence.
We show that in an ordered matroid the partial derivative \partial^{p+q}t/\partialx^p\partialyq of the Tutte polynomial is p!q! times the generating function of activities of subsets with corank p and nullity q. More generally, this property holds for the 3-variable Tutte polynomial of a matroid perspective.
Iris Recognition Systems are ocular- based biometric devices used primarily for security reasons. The complexity and the randomness of the Iris, amongst various other factors, ensure that this biometric system is inarguably an exact and reliable method of identification. The algorithm is responsible for automatic localization and segmentation of boundaries using circular Hough Transform, noise reductions, image enhancement and feature extraction across numerous distinct images present in the database. This paper delves into the various kinds of techniques required to approximate the pupillary and limbic boundaries of the enrolled iris image, captured using a suitable image acquisition device and perform feature extraction on the normalized iris image with the help of Haar Wavelets to encode the input data into a binary string format. These techniques were validated using images from the CASIA database, and various other procedures were also tried and tested.
We present a solid relationship between the neutral hydrogen (HI) disk mass and the stellar disk mass of late-type galaxies in the local universe. This relationship is derived by comparing the stellar disk mass function from the Sloan Digital Sky Survey and the HI mass function from the HI Parkes All Sky Survey (HIPASS). We find that the HI mass in late-type galaxies tightly correlates with the stellar mass over three orders of magnitude in stellar disk mass. We cross-check our result with that obtained from a sample of HIPASS objects for which the stellar mass has been obtained by inner kinematics. In addition, we derive the HI versus halo mass relationship and the dependence of all the baryonic components in spirals on the host halo mass. These relationships bear the imprint of the processes ruling galaxy formation, and highlight the inefficiency of galaxies both in forming stars and in retaining their pristine HI gas.
We derive a theory for transmission through disordered finite superlattices in which the interface roughness scattering is treated by disorder averaging. This procedure permits efficient calculation of the transmission thr ough samples with large cross-sections. These calculations can be performed utilizing either the Keldysh or the Landauer-B\"uttiker transmission formalisms, both of which yield identical equations. For energies close to the lowest miniband, we demonstrate the accuracy of the computationally efficient Wannier-function approximation. Our calculations indicate that the transmission is strongly affected by interface roughness and that information about scale and size of the imperfections can be obtained from transmission data.
In this paper we suggest an implementation of Runge's method for solving Diophantine equations satisfying Runge's condition. In this implementation we avoid the use of Puiseux series and algebraic coefficients.
In this work, the so-called Eshelbian or configurational mechanics of quasicrystals is presented. Quasicrystals are considered as a prototype of novel materials. Material balance laws for quasicrystalline materials with dislocations are derived in the framework of generalized incompatible elasticity theory of quasicrystals. Translations, scaling transformations as well as rotations are examined; the latter presents particular interest due to the quasicrystalline structure. This derivation provides important quantities of the Eshelbian mechanics, as the Eshelby stress tensor, the scaling flux vector, the angular momentum tensor, the configurational forces (Peach-Koehler force, Cherepanov force, inhomogeneity force or Eshelby force), the configurational work and the configurational vector moments for dislocations in quasicrystals. The corresponding $J$-, $M$-, and $L$-integrals for dislocation loops and straight dislocations in quasicrystals are derived and discussed. Moreover, the explicit formulas of the $J$-, $M$-, and $L$-integrals for parallel screw dislocations in one-dimensional hexagonal quasicrystals are obtained. Through this derivation, the physical interpretation of the $J$-, $M$-, and $L$-integrals for dislocations in quasicrystals is revealed and their connection to the Peach-Koehler force, the interaction energy and the rotational vector moment (torque) of dislocations in quasicrystals is established.
The old pulsar PSR B0943+10 (P=1.1 s, characteristic age tau=5 Myr) is the best example of mode-switching radio pulsar. Its radio emission alternates between a highly organized state with regular drifting subpulses (B mode) and a chaotic emission pattern (Q mode). We present the results of XMM-Newton observations showing that the X-ray properties of PSR B0943+10 depend on its radio state (Hermsen et al. 2013). During the radio fainter state (Q mode) the X-ray flux is more than a factor two larger than during the B-mode and X-ray pulsations with about 50% pulsed fraction are detected. The X-ray emission of PSR B0943+10 in the B-mode is well described by thermal emission with blackbody temperature kT=0.26 keV coming from a small hot spot with luminosity of 7x10^28 erg/s, in good agreement with the prediction of the partially screened gap model, which also explains the properties of the radio emission in this mode. We derived an upper limit of 46% on the X-ray pulsed fraction in the B-mode, consistent with the geometry and viewing angle of PSR B0943+10 inferred from the radio data. The higher flux observed during the Q-mode is consistent with the appearance of an additional component with a power-law spectrum with photon index 2.2. We interpret it as pulsed non-thermal X-rays produced in the star magnetosphere. A small change in the beaming pattern or in the efficiency of acceleration of the particles responsible for the non-thermal emission can explain the reduced flux of this component during the radio B-mode.
Optical observations of nova V1974 Cygni (Cygni 1992), spanning a 4 year period, have been used to study its spectroscopic evolution. The data cover a wavelength range from $\sim 3200 - 8000$ \AA and follows the nebular evolutionary phase of the ejecta. We have modeled the integrated fluxes by means of the photoionization code CLOUDY. The models were run at a {\it fixed} abundance value for the most prominent elements (i.e. H, He, C, O, N, Ne, Fe, etc) over the entire time sequence. It is possible to constrain from this simple model some of the physical conditions of the gaseous emitting region, like temperature and density. Compared with previous studies of the gas abundances of the heavy elements, we found that smaller enhancements of S, N and Ar, and comparable values for O and Fe, are able to reproduce the observations. The time evolution of the surface temperature of the ionizing source and the high-ionization iron lines [Fe VII] 6087 \AA and [Fe X] 6374 \AA, is similar to what it is observed in the soft X-rays. The early line profiles can be reproduced using a simple kinematical model consisting of an equatorial ring and polar caps, expanding at a velocity of $\sim 1100$ km/s. This simple model also approximates the structure of the resolved shell observed by HST. Considering the complicated structure of the shell, the lack of well defined values of its gas density and our limited knowledge of the time evolution of the surface temperature of the photoionization source, the comparison between models and observations agrees remarkably well.
A new approach is suggested which allows to describe phenomenologically arbitrary topologies of the Universe. It consists in a generalizaton of third quantization. This quantization is carried out for the case of asymptotic closeness to a cosmological singularity. It is also pointed out that suggested approach leads to a modification of the ordinary quantum field theory. In order to show this modification we consider the example of a free massless scalar field.
We establish here a Quantitative Central Limit Theorem (in Wasserstein distance) for the Euler-Poincar\'{e} Characteristic of excursion sets of random spherical eigenfunctions in dimension 2. Our proof is based upon a decomposition of the Euler-Poincar\'{e} Characteristic into different Wiener-chaos components: we prove that its asymptotic behaviour is dominated by a single term, corresponding to the chaotic component of order two. As a consequence, we show how the asymptotic dependence on the threshold level $u$ is fully degenerate, i.e., the Euler-Poincar\'{e} Characteristic converges to a single random variable times a deterministic function of the threshold. This deterministic function has a zero at the origin, where the variance is thus asymptotically of smaller order. Our results can be written as an asymptotic second-order Gaussian Kinematic Formula for the excursion sets of Gaussian spherical harmonics.
Unitary representations of the fundamental group of a Kahler manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to polystable Higgs bundles. In this paper we find the objects corresponding to affine representations: the linear part gives a Higgs bundle and the translation part corresponds to an element of a generalized de Rham cohomology.
We study the phases of a spin system on the Kagome lattice with nearest-neighbor $XXZ$ interactions with anisotropy ratio $\Delta$ and Dzyaloshinsky-Moriya interactions with strength $D$. In the classical limit where the spin $S$ at each site is very large, we find a rich phase diagram of the ground state as a function of $\Delta$ and $D$. There are five distinct phases which correspond to different ground state spin configurations in the classical limit. We use spin wave theory to find the bulk energy bands of the magnons in some of these phases. We also study a strip of the system which has infinite length and finite width; we find modes which are localized on one of the edges of the strip with energies which lie in the gaps of the bulk modes. In the ferromagnetic phase in which all the spins point along the $+ \hat z$ or $- \hat z$ direction, the bulk bands are separated from each other by finite energy gaps. This makes it possible to calculate the Berry curvature at all momenta, and hence the Chern numbers for every band; the number of edge states is related to the Chern numbers. Interestingly, we find that there are four different regions in this phase where the Chern numbers are different. Hence there are four distinct topological phases even though the ground state spin configuration is identical in all these phases. We calculate the thermal Hall conductivity of the magnons as a function of the temperature in the above ferromagnetic phase; we find that this can distinguish between the various topological phases. These results are valid for all values of $S$.In the other phases, there are no gaps between the different bands; hence the edge states are not topologically protected.
We establish a Liouville type theorem for the fractional Lane-Emden system:   \begin{eqnarray*} \left\{\begin{array}{l@{\quad }l} (-\Delta)^\alpha u=v^q&{\rm in}\,\,\R^N,\\ (-\Delta)^\alpha v=u^p&{\rm in}\,\,\R^N,   \end{array}   \right.   \end{eqnarray*}   where $ \alpha\in(0,1) $, $ N>2\alpha $ and $ p,q $ are positive real numbers and in an appropriate new range.   To prove our result we will use the local realization of fractional Laplacian, which can be constructed as Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre \cite{CS}. Our proof is based on a monotonicity argument for suitable transformed   functions and the method of moving planes in an infinity half cylinder based on some maximum principles which obtained by some barrier functions and a coupling argument using fractional Sobolev trace inequality.
In this paper we show that quotients of smooth projective toric varieties by $\mu_p$ in positive characteristics $p$ are toric varieties.
We study the minimization of ADMs (Add-Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all-to-all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor $C$ and $N$, the size of the ring. We first study exhaustively the cases C=1, $C = 2$, and C=3, providing improved lower bounds, optimal constructions for several infinite families, as well as asymptotically optimal constructions and approximations. We then study the case $C>3$, focusing specifically on the case $C = k(k+1)/2$ for some $k \geq 1$. We give optimal decompositions for several congruence classes of $N$ using the existence of some combinatorial designs. We conclude with a comparison of the cost functions in unidirectional and bidirectional WDM rings.
A number of current and future experiments aim to detect the reionization of neutral hydrogen by the first stars and galaxies in the Universe via the redshifted 21cm line. Using the \textsc{BlueTides} simulation, we investigate the measurement of an \textit{average} ionised region towards the beginning of reionization by stacking redshifted 21cm images around optically identified bright galaxies using mock observations. We find that with an SKA 1000 hour observation, assuming perfect foreground subtraction, a $5\sigma$ detection of a stacked HII region can be made with 30 images around some of the brightest galaxies in \textsc{bluetides} (brighter than $M_{UV} < -22.75$) at $z=9$ (corresponding to a neutral fraction of 90.1 \% in our model). We present simulated relationships between the UV magnitude of galaxies, the sizes of the ionised regions they reside in, and the shape of the stacked profiles. These mock observations can also distinguish between scenarios where the IGM is in net emission or absorption of 21cm photons. Once 21cm foreground contamination is included, we find that even with up to 200 images around these rare, bright galaxies, only a tentative $> 1\sigma$ detection will be possible. However, partial foreground subtraction substantially improves signal-to-noise. For example, we predict that reducing the area of Fourier space dominated by foregrounds by 50 (80) percent will allow $> 3\sigma$ ($> 5\sigma$) detections of ionised regions at $z=9$.
In this paper we classify codimension 1 Mukai foliations on complex projective manifolds
We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburg's $\Psi$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point. We consider three versions of the theory, depending on the way one determines its parameters from the experimental measurements. We present exact results for the behavior of the order parameter profiles and of the Casimir force within this theory, which is characterized by $d=3$, $\nu=2/3$ and $\beta=1/3$, where $d$ is the bulk spatial dimension and $\nu$ and $\beta$ are the usual critical exponents. In addition, we revisit relevant experiments \cite{GC99} and \cite{GSGC2006} in terms of our findings. We find reasonably good agreement between our theoretical predictions and the experimental data. We demonstrate analytically that our calculated force is attractive. The position of the extremum is predicted to be at $x_{\rm min}=\pi$, with $x=(L/\xi_0)(T/T_\lambda-1)^{1/\nu}$, which value effectively coincides with the experimental finding $x_{\rm min}=3.2\pm 0.18$. Here $L$ is the thickness of the film, $T_\lambda$ is the bulk critical temperature and $\xi_0$ is the correlation length amplitude of the system for temperature $T>T_\lambda$. The theoretically predicted position of the minimum does not depend on the one adjustable parameter, $M$, entering the theory.
This comment re-examines the origin of structure seen in the computed specific heat of finite nuclei. In a recent paper, Civitarese and Schvellinger suggest that such structure is due to model-space truncation in the calculations. We reaffirm our conclusion that the structure is caused by a collective-to-non-collective phase transformation at low temperatures, signaled by a change in the nuclear level density below 10 MeV excitation energy.
We analyze the real-time dynamics of a quantum two-state system in the presence of nonequilibrium quantum fluctuations. The latter are generated by a coupling of the two-state system to a single electronic level of a quantum dot which carries a nonequilibrium tunneling current. We restrict to the sequential tunneling regime and calculate the dynamics of the two-state system, of the dot population, and of the nonequilibrium charge current on the basis of a diagrammatic perturbative method valid for a weak tunneling coupling. We find a nontrivial dependence of the relaxation and dephasing rates of the two-state system due to the nonequilibrium fluctuations which is directly linked to the structure of the unperturbed central system. In addition, a Heisenberg-Langevin-equation of motion allows us to calculate the correlation function of the nonequilibrium fluctuations. By this, we obtain a generalized nonequilibrium fluctuation relation which includes the equilibrium fluctuation-dissipation theorem. A straightforward extension to the case with a time-periodic ac voltage is shown.
The effect of the interface roughness on the spin injection from a ferromagnet into a semiconductor is studied theoretically. Even a small interface irregularity can lead to a significant enhancement of the injection efficiency. When a typical size of the irregularity, a, is within a domain lambda_F << a << lambda_N, where lambda_F and lambda_N are the spin-diffusion lengths in the ferromagnet and semiconductor, respectively, the geometrical enhancement factor is ~lambda_N. The origin of the enhancement is the modification of the local electric field on small scales ~a near the interface. We demonstrate the effect of enhancement by considering a number of analytically solvable examples of injection through curved ferromagnet-semiconductor interfaces. For a generic curved interface the enhancement factor is ~lambda_N / R, where R is the local radius of curvature.
We report electronic transport measurements on two-dimensional electron gases in a Ga[Al]As heterostructure with an embedded layer of InAs self-assembled quantum dots. At high InAs dot densities, pronounced Altshuler-Aronov-Spivak magnetoresistance oscillations are observed, which indicate short-range ordering of the potential landscape formed by the charged dots and the strain fields. The presence of these oscillations coincides with the observation of a metal-insulator transition, and a maximum in the electron mobility as a function of the electron density. Within a model based on correlated disorder, we establish a relation between these effects.
The long term evolution of ULX with their spectral and luminosity variations in time give important clues on the nature of ULX and on the accretion process that powers them. We report here the results of a Swift-XRT 6-year monitoring campaign of the closest example of a persistent ULX, M33 X-8, that extends to 16 years the monitoring of this source in the soft X-rays. The luminosity of this source is a few 10^39 erg/s, marking the faint end of the ULX luminosity function. We analysed the set of 15 observations collected during the Swift monitoring. We searched for differences in the spectral parameters at different observing epochs, adopting several models commonly used to fit the X-ray spectra of ULX. The source exhibits flux variations of the order of 30%. No significant spectral variations are observed along the monitoring. The average 0.5-10 keV spectrum can be well described by a thermal model, either in the form of a slim disk, or as a combination of a Comptonized corona and a standard accretion disk.
We study the modulational instability of periodic traveling waves for a class of Hamiltonian systems in one spatial dimension. We examine how the Jordan block structure of the associated linearized operator bifurcates for small values of the Floquet exponent to derive a criterion governing instability to long wavelengths perturbations in terms of the kinetic and potential energies, the momentum, the mass of the underlying wave, and their derivatives. The dispersion operator of the equation is allowed to be nonlocal, for which Evans function techniques may not be applicable. We illustrate the results by discussing analytically and numerically equations of Korteweg-de Vries type.
Minor mergers of galaxies are expected to be common in a hierarchical cosmology such as $\Lambda$CDM and have the potential to significantly affect galactic structure. In this paper we dissect the case-by-case outcome from a set of numerical simulations of a single satellite elliptical galaxy accreting onto a massive elliptical galaxy. We take care to explore cosmologically relevant orbital parameters and to set up realistic initial galaxy models that include all three relevant dynamical components: dark matter halos, stellar bulges, and central massive black holes. The effects of several different parameters are considered, including orbital energy and angular momentum, satellite density and inner density profile, satellite-to-host mass ratio, and presence of a black hole at the center of the host. Black holes play a crucial role in protecting the shallow stellar cores of the hosts, as satellites merging onto a host with a central black hole are more strongly disrupted than those merging onto hosts without black holes. Orbital parameters play an important role in determining the degree of disruption: satellites on less bound or more eccentric orbits are more easily destroyed than those on more bound or more circular orbits as a result of an increased number of pericentric passages and greater cumulative effects of gravitational shocking and tidal stripping. In addition, satellites with densities typical of faint elliptical galaxies are disrupted relatively easily, while denser satellites can survive much better in the tidal field of the host. Over the range of parameters explored, we find that the accretion of a single satellite elliptical galaxy can result in a broad variety of changes, in both signs, in the surface brightness profile and color of the central part of an elliptical galaxy.