ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the 2D Muskat equation for the interface between two constant density fluids in an incompressible porous medium, with velocity given by Darcy's law. We establish that as long as the slope of the interface between the two fluids remains bounded and uniformly continuous, the solution remains regular. The proofs exploit the nonlocal nonlinear parabolic nature of the equations through a series of nonlinear lower bounds for nonlocal operators. These are used to deduce that as long as the slope of the interface remains uniformly bounded, the curvature remains bounded. The nonlinear bounds then allow us to obtain local existence for arbitrarily large initial data in the class $W^{2,p}$, $1<p\leq \infty$. We provide furthermore a global regularity result for small initial data: if the initial slope of the interface is sufficiently small, there exists a unique solution for all time.
A new Schottky-gate Bipolar Mode Field Effect Transistor (SBMFET) is proposed and verified by two-dimensional simulation. Unlike in the case of conventional BMFET, which uses deep diffused p+-regions as the gate, the proposed device uses the Schottky gate formed on the silicon planar surface for injecting minority carriers into the drift region. The SBMFET is demonstrated to have improved current gain, identical breakdown voltage and ON-voltage drop when compared to the conventional BMFET. Since the fabrication of the SBMFET is much simpler and obliterates the need for deep thermal diffusion of P+-gates, the SBMFET is expected to be of great practical importance in medium-power high-current switching applications.
In this work we review the efforts that have been done to study the excitation of the standing fast kink body mode in coronal loops. We mainly focus on the time-dependent problem, which is appropriate to describe flare or CME induced kink oscillations. The analytical and numerical studies in slab and cylindrical loop geometries are reviewed. We discuss the results from very simple one-dimensional models to more realistic (but still simple) loop configurations. We emphasise how the results of the initial value problem complement the eigenmode calculations. The possible damping mechanisms of the kink oscillations are also discussed.
We consider 1+1 D theories which are free everywhere except for cosine and magnetic interactions on the boundary. These theories arise in dissipative quantum systems, open string theory, and, in special cases, tunneling in quantum Hall systems. These boundary systems satisfy an approximate SL(2,Z) symmetry as a function of flux per unit cell and dissipation. At special multicritical points, they also satisfy a set of reparametrization Ward identities and have homogeneous, piecewise-linear correlation functions in momentum space. In this paper, we use these symmetries to find exact solutions for some of the correlation functions. We also comment on the form of the correlation functions in general, and verify that the SL(2,Z) duality transformation between different critical points is satisfied exactly in all cases where the full solution is known.
We give finite presentations for the fundamental group of moduli stacks of smooth Weierstrass curves over complex projective space P^n which extend the classical result for elliptic curves to positive dimensional base. We thus get natural generalisations of SL_2(Z) and pave the way to understanding the fundamental group of moduli stacks of elliptic surfaces in general.   Our approach exploits the natural involution on Weierstrass curves and the identification of its fixed loci with smooth hypersurfaces in an appropriate linear system on a projective line bundle over P^n. The fundamental group of the corresponding discriminant complement can be presented in terms of finitely many generators and relations using methods in the Zariski tradition, which were sucessfully elaborated in mathAG/0602371.
It has been first proved the effect of grains merging during drawing deformation. This was done with example of producing a steel wire from rod manufactured by rolling with shear technology and was shown not only grain refinement but its merging as well. The result obtained in current work has fundamental importance; it reveals new mechanism of the "recrystallization" which takes place without diffusion actions owing to the mechanical impact.
Linear time series analysis, mainly the Fourier transform based methods, has been quite successful in extracting information contained in the ever-modulating light curves (Lcs) of active galactic nuclei, and thereby contribute in characterizing the general features of supermassive black hole systems. In particular, the statistical properties of $\gamma$-ray variability of blazars are found to be fairly represented by flicker noise in the temporal frequency domain. However, these conventional methods have not been able to fully encapsulate the richness and the complexity displayed in the light curves of the sources. In this work, to complement our previous study on the similar topic, we perform non-linear time series analysis of the decade-long Fermi/LAT observations of 20 $\gamma$-ray bright blazars. The study is motivated to address one of the most relevant queries that whether the dominant dynamical processes leading to the observed $\gamma$-ray variability are of deterministic or stochastic nature. For the purpose, we perform Recurrence Quantification Analysis of the blazars and directly measure the quantities which suggest that the dynamical processes in blazar could be a combination of deterministic and stochastic processes, while some of the source light curves revealed significant deterministic content. The result with possible implication of strong disk-jet connection in blazars could prove to be significantly useful in constructing models that can explain the rich and complex multi-wavelength observational features in active galactic nuclei. In addition, we estimate the dynamical timescales, so called "trapping timescales", in the order of a few weeks.
We show that the new type of "non-metric" gravity theories introduced independently by Bengtsson and Krasnov can in fact be reexpressed explicitely as a metrical theory coupled to an auxiliary field. We unravel why such theories possess only one propagating graviton by looking at the quadratic perturbation around a fixed solution. And we give a general construction principle with a new class of example of such modified gravity theories still possessing only two propagating degrees of freedom.
The production of a printed product involves three stages: prepress, the printing process (press) itself, and finishing (post press). There are various types of equipments (printers, scanners) and various qualities image are present in the market. These give different color rendering each time during reproduction. So, a color key tool has been developed keeping Color Management Scheme (CMS) in mind so that during reproduction no color rendering takes place irrespective of use of any device and resolution level has also been improved.
We study the suppression of qubit dephasing through Uhrig dynamical decoupling (UDD) in nontrivial environments modeled within the spin-boson formalism. In particular, we address the case of (i) a qubit coupled to a bosonic bath with power-law spectral density, and (ii) a qubit coupled to a single harmonic oscillator that dissipates energy into a bosonic bath, which embodies an example of a structured bath for the qubit. We then model the influence of random time jitter in the UDD protocol by sorting pulse-application times from Gaussian distributions centered at appropriate values dictated by the optimal protocol. In case (i) we find that, when few pulses are applied and a sharp cutoff is considered, longer coherence times and robust UDD performances (against random timing errors) are achieved for a super-Ohmic bath. On the other hand, when an exponential cutoff is considered a super-Ohmic bath is undesirable. In case (ii) the best scenario is obtained for an overdamped harmonic motion. Our study provides relevant information for the implementation of optimized schemes for the protection of quantum states from decoherence.
In this paper we show that in two-body scattering the scattering matrix at a fixed energy determines real-valued exponentially decreasing potentials. This result has been proved by Novikov previously, see also the work of Novikov and Khenkin using a d-bar-equation. We present a different method, which combines a density argument and real analyticity in part of the complex momentum. The latter has been noted by Novikov and Khenkin; here we give a short proof using contour deformations.   In the addendum to the paper we also supply a reference to the work of Eskin and Ralston that did not appear in the published paper since we were unaware of the relevant aspects of their work.
A (positive definite and non-classic integral) quadratic form is called strongly $s$-regular if it satisfies a strong regularity property on the number of representations of squares of integers. In this article, we prove that for any integer $k \ge 2$, there are only finitely many isometry classes of strongly $s$-regular quadratic forms with rank $k$ if the minimum of the nonzero squares that are represented by them is fixed.
In the last years, automated segmentation has become a necessary tool for volume electron microscopy (EM) imaging. So far, the best performing techniques have been largely based on fully supervised encoder-decoder CNNs, requiring a substantial amount of annotated images. Domain Adaptation (DA) aims to alleviate the annotation burden by 'adapting' the networks trained on existing groundtruth data (source domain) to work on a different (target) domain with as little additional annotation as possible. Most DA research is focused on the classification task, whereas volume EM segmentation remains rather unexplored. In this work, we extend recently proposed classification DA techniques to an encoder-decoder layout and propose a novel method that adds a reconstruction decoder to the classical encoder-decoder segmentation in order to align source and target encoder features. The method has been validated on the task of segmenting mitochondria in EM volumes. We have performed DA from brain EM images to HeLa cells and from isotropic FIB/SEM volumes to anisotropic TEM volumes. In all cases, the proposed method has outperformed the extended classification DA techniques and the finetuning baseline. An implementation of our work can be found on https://github.com/JorisRoels/domain-adaptive-segmentation.
The mechanism accelerating cosmic rays in the Milky Way Galaxy and galaxy clusters is identified and described. The acceleration of cosmic rays is a purely electrostatic process which operates up to the maximum energies of $10^{23}$ eV in galaxy clusters. Galactic cosmic rays are accelerated in a pervasive electrostatic field active in the whole Galaxy except in restricted regions shielded by interstellar and stellar plasmas as, for instance, the region occupied by the solar system. It is proved that the energy spectrum of the cosmic radiation in the Milky Way Galaxy, in the region where the solar system resides, has a constant spectral index comprised between 2.64-2.68 and the maximum energies of Galactic protons are $3.0 \times 10^{19}$ eV. The agreement of these results with the experimental data is discussed in detail and underlined. The various physical processes that maintain the stability of the electrostatic structure in the Milky Way Galaxy are the same that generate the Galactic magnetic field. Accordingly, the intensity, orientation and direction of the Galactic magnetic field are evaluated. The results of the calculation are compared with the observational data, optical and mostly radio astronomy data. The accord of the intensity, orientation and direction of the observed magnetic field with calculation is excellent.
We study a class of fractional semilinear elliptic equations and formulate the corresponding Calder\'on problem. We determine the nonlinearity from the exterior partial measurements of the Dirichlet-to-Neumann map by using first order linearization and the Runge approximation property.
Recent geometric methods need reliable estimates of 3D motion parameters to procure accurate dense depth map of a complex dynamic scene from monocular images \cite{kumar2017monocular, ranftl2016dense}. Generally, to estimate \textbf{precise} measurements of relative 3D motion parameters and to validate its accuracy using image data is a challenging task. In this work, we propose an alternative approach that circumvents the 3D motion estimation requirement to obtain a dense depth map of a dynamic scene. Given per-pixel optical flow correspondences between two consecutive frames and, the sparse depth prior for the reference frame, we show that, we can effectively recover the dense depth map for the successive frames without solving for 3D motion parameters. Our method assumes a piece-wise planar model of a dynamic scene, which undergoes rigid transformation locally, and as-rigid-as-possible transformation globally between two successive frames. Under our assumption, we can avoid the explicit estimation of 3D rotation and translation to estimate scene depth. In essence, our formulation provides an unconventional way to think and recover the dense depth map of a complex dynamic scene which is incremental and motion free in nature. Our proposed method does not make object level or any other high-level prior assumption about the dynamic scene, as a result, it is applicable to a wide range of scenarios. Experimental results on the benchmarks dataset show the competence of our approach for multiple frames.
Diffusion-limited reactions (DLR) are usually described within the Smoluchowski theory, which neglects interactions between the diffusing components. We propose a first extension of such frame- work that incorporates excluded-volume effects, considering hard diffusing agents in the presence of an absorbing sink. For large values of the absorber-to-diffuser size ratio Rs, the encounter rate obtained from the simulations is in very good agreement with a simple generalization of the Smolu- chowski equation at high densities. Reducing Rs, the rate gets substantially depressed at interme- diate packing and become even non-monotonic for Rs << 1. Concurrently with the saturation of the rate, stationary density waves set in close to the absorbing center. A mean-field, effective-potential analysis of the Smoluchowski equation under crowding sheds light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of non-reacting impurities can equally slow down dramatically the reaction.
We illustrate a step towards the construction of a power counting in energy-density-functional (EDF) theories, by analyzing the equations of state (EOSs) of both symmetric and neutron matter. Within the adopted strategy, next-to-leading order (NLO) EOSs are introduced which contain renormalized first-order-type terms and an explicit second-order finite part. Employing as a guide the asymptotic behavior of the introduced renormalized parameters, we focus our analysis on two aspects: (i) With a minimum number of counterterms introduced at NLO, we show that each energy contribution entering in the EOS has a regular evolution with respect to the momentum cutoff (introduced in the adopted regularization procedure) and is found to converge to a cutoff-independent curve. The convergence features of each term are related to its Fermi-momentum dependence. (ii) We find that the asymptotic evolution of the second-order finite-part coefficients is a strong indication of a perturbative behavior, which in turns confirms that the adopted strategy is coherent with a possible underlying power counting in the chosen Skyrme-inspired EDF framework.
Y CVn is a carbon star surrounded by a detached dust shell that has been imaged by the Infrared Space Observatory at 90 microns. With the Nancay Radio Telescope we have studied the gaseous counterpart in the 21-cm HI emission line. New data have been acquired and allow to improve the signal to noise ratio on this line. The high spectral resolution line profiles obtained at the position of the star and at several offset positions set strong constraints on the gas temperature and kinematics within the detached shell; the bulk of the material should be at ~ 100-200 K and in expansion at ~ 1-2 km/s. In addition, the line profile at the central position shows a quasi-rectangular pedestal that traces an 8 km/s outflow of ~ 1.0 10^-7 Msol/yr, stable for about 2 10^4 years, which corresponds to the central outflow already studied with CO rotational lines. We present a model in which the detached shell results from the slowing-down of the stellar wind by surrounding matter. The inner radius corresponds to the location where the stellar outflow is abruptly slowed down from ~ 8 km/s to 2 km/s (termination shock). The outer radius corresponds to the location where external matter is compressed by the expanding shell (bow shock). In this model the mass loss rate of Y CVn has been set constant, at the same level of 1.0 10^-7 Msol/yr, for ~ 4.5 10^5 years. The gas temperature varies from ~ 1800 K at the inner limit to 165 K at the interface between circumstellar matter and external matter. Our modelling shows that the presence of a detached shell around an AGB star may not mean that a drastic reduction of the mass loss rate has occurred in the past. The inner radius of such a shell might only be the effect of a termination shock rather than of an interruption of the mass loss process.
We assume the Riemann Hypothesis and an quantitative form of the Twin Prime Conjecture, and obtain an asymptotic formula for the second moment of $S(T)$ with better error term.
In light of the discovery of a Higgs-like particle at the LHC, we revisit the status of the precision electroweak data, focusing on two discrepant observables: 1) the long-standing 2.4 sigma deviation in the forward-backward asymmetry of the bottom quark A_{FB}^b, and 2) the 2.3 sigma deviation in R_b, the ratio of the Z \rightarrow b \bar b partial width to the inclusive hadronic width, which is now in tension after a recent calculation including new two-loop electroweak corrections. We consider possible resolutions of these discrepancies. Taking the data at face value, the most compelling scenario is that new physics directly affects A_{FB}^b and R_b, bringing the prediction into accord with the measured values. We propose a modified `Beautiful Mirrors' scenario which contains new vector-like quarks that mix with the b quark, modifying the Z b\bar b vertex and thus correcting A_{FB}^b and R_b. We show that this scenario can lead to modifications to the production rates of the Higgs boson in certain channels, and in particular a sizable enhancement in the diphoton channel. We also describe additional collider tests of this scenario.
We obtain electric charge quantization in the context of models based on the gauge symmetry group SU(3) X SU(4) X U(1). The gauge models studied include three families to cancel out anomalies and a set of scalar fields to break spontaneously the symmetry. To show the electric charge quantization, we use clasical symmetry conditions and quantum quiral anomaly conditions.
This study investigates the topological behavior of a continuous elastic phononic structure characterized by a 3-term Kekul\'e distortion. The elastic waveguide consists of a hexagonal unit cell whose geometric dimensions are intentionally perturbed according to a generalized Kekul\'e scheme. The resulting structure exhibits an effective Hamiltonian that resembles a quantum spin Hall system, hence suggesting that the waveguide can support helical topological edge states. Using first-principles calculations, we show the existence of nondegenerate pseudospin states and a very peculiar 6-lobe pseudospin texture and Berry curvature pattern. Important insights are also provided concerning the topological states in the Kekul\'e lattice, so far considered indistinguishable, and their critical role in enabling unique gapless edge states, typically not achievable in phononic systems.
We present an octonionic N=1 superfield action that reproduces in components the action of Bagger and Lambert for M2 branes. By giving an expectation value to one of the scalars we obtain the maximally supersymmetric superfield action for D2 branes.
Machine-learning potentials for materials, namely the moment tensor potentials (MTPs), were validated using experimental EXAFS spectra for the first time. The MTPs for four metals (bcc W and Mo, fcc Cu and Ni) were obtained by the active learning algorithm of fitting to the results of the calculations using density functional theory (DFT). The MTP accuracy was assessed by comparing metal K-edge EXAFS spectra obtained experimentally and computed from the results of molecular dynamics (MD) simulations. The sensitivity of the method to various aspects of the MD and DFT models was demonstrated using Ni as an example. Good agreement was found for W, Mo and Cu using the recommended PAW pseudopotentials, whereas a more accurate pseudopotential with 18 valence electrons was required for Ni to achieve a similar agreement. The use of EXAFS spectra allows one to estimate the MTP ability in reproducing both average and dynamic atomic structures.
Aims. Many recent observations of pulsars and magnetars can be interpreted in terms of neutron stars (NS) with multipole electromagnetic fields. As a first approximation, we investigate the multipole magnetic and electric fields in the environment of a rotating star when this environment is deprived of plasma. Methods. We compute a multipole expansion of the electromagnetic field in vacuum for a given magnetic field on the conducting surface of the rotating star. Then, we consider a few consequences of multipole fields of pulsars. Results. We provide an explicit form of the solution. For each spherical harmonic of the magnetic field, the expansion contains a finite number of terms. A multipole magnetic field can provide an explanation for the stable sub-structures of pulses, and they offer a solution to the problem of current closure in pulsar magnetospheres. Conclusions. This computation generalises the widely used model of a rotating star in vacuum with a dipole field. It can be especially useful as a first approximation to the electromagnetic environment of a compact star, for instance a neutron star, with an arbitrarily magnetic field.
Various optimal estimates for solutions of the Laplace, Lam\'e and Stokes equations in multidimensional domains, as well as new real-part theorems for analytic functions are obtained.
In 1977 Stanley conjectured that the $h$-vector of a matroid independence complex is a pure $O$-sequence. In this paper we use lexicographic shellability for matroids to motivate a combinatorial strengthening of Stanley's conjecture. This suggests that a pure $O$-sequence can be constructed from combinatorial data arising from the shelling. We then prove that our conjecture holds for matroids of rank at most four, settling the rank four case of Stanley's conjecture. In general, we prove that if our conjecture holds for all rank $d$ matroids on at most $2d$ elements, then it holds for all matroids.
We study (p,q)=(2,4k) minimal superstrings within the minimal superstring field theory constructed in hep-th/0611045. We explicitly give a solution to the W_{1+\infty} constraints by using charged D-instanton operators, and show that the (m,n)-instanton sector with m positive-charged and n negative-charged ZZ-branes is described by an (m+n)\times (m+n) supermatrix model. We argue that the supermatrix model can be regarded as an open string field theory on the multi ZZ-brane system.