ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn-Hilliard-Oono equation in the whole space R^3 with the non-linearity of the sub-quintic growth rate. Moreover, the dissipativity and the existence of a smooth global attractor in the naturally defined energy space is also verified. The result is crucially based on the Strichartz estimates for the linear Scroedinger equation in R^3.
We present the global optical photometry of 246 galaxies in the Local Volume Legacy (LVL) survey. The full volume-limited sample consists of 258 nearby (D < 11 Mpc) galaxies whose absolute B-band magnitude span a range of -9.6 < M_B < -20.7 mag. A composite optical (UBVR) data set is constructed from observed UBVR and SDSS ugriz imaging, where the ugriz magnitudes are transformed into UBVR. We present photometry within three galaxy apertures defined at UV, optical, and IR wavelengths. Flux comparisons between these apertures reveal that the traditional optical R25 galaxy apertures do not fully encompass extended sources. Using the larger IR apertures we find color-color relationships where later-type spiral and irregular galaxies tend to be bluer than earlier-type galaxies. These data provide the missing optical emission from which future LVL studies can construct the full panchromatic (UV-optical-IR) spectral energy distributions.
We have completed a robotic wide-angle imaging survey of the southern sky (declination less than +15 degrees) at 656.3 nm wavelength, the H-alpha emission line of hydrogen. Each image of the resulting Southern H-Alpha Sky Survey Atlas (SHASSA) covers an area of the sky 13 degrees square at an angular resolution of approximately 0.8 arcminute, and reaches a sensitivity level of 2 rayleigh (1.2 x 10^-17 erg cm^-2 s^-1 arcsec^-2) per pixel, corresponding to an emission measure of 4 cm^-6 pc, and to a brightness temperature for microwave free-free emission of 12 microkelvins at 30 GHz. Smoothing over several pixels allows features as faint as 0.5 rayleigh to be detected.
Recent observations demonstrated that emerging flux regions, which constitute the early stage of solar active regions, consist of emergence of numerous small-scale magnetic elements. They in turn interact, merge, and form mature sunspots. However, observations of fine magnetic structures on photosphere with sub-arcsecond resolution are very rare due to limitations of observing facilities. In this work, taking advantage of the high resolution of the 1.6 m Goode Solar Telescope, we jointly analyze vector magnetic fields, continuum images, and H{\alpha} observations of NOAA AR 12665 on 2017 July 13, with the goal of understanding the signatures of small-scale flux emergence, as well as their atmospheric responses as they emerge through multiple heights in photosphere and chromosphere. Under such a high resolution of 0.1" to 0.2", our results confirm two kinds of small-scale flux emergence: magnetic flux sheet emergence associated with the newly forming granules, and the traditional magnetic flux loop emergence. With direct imaging in the broadband TiO, we observe that both types of flux emergence are associated with darkening of granular boundaries, while only flux sheets elongate granules along the direction of emerging magnetic fields and expand laterally. With a life span of 10--15 minutes, the total emerged vertical flux is in order of 10$^{18}$ Mx for both types of emergence. The magnitudes of the vertical and horizontal fields are comparable in the flux sheets, while the former is stronger in flux loops. H{\alpha} observations reveal transient brightenings in the wings in the events of magnetic loop emergence, which are most probably the signatures of Ellerman bombs.
SiO maser emission occurs in the extended atmosphere of evolved stars and can be studied at high angular resolution. Very long baseline interferometry (VLBI) observations of Mira variables indicate that SiO masers are significantly linearly polarized with linear polarization fraction up to 100%. However, no information is available at high angular resolution for SiO masers in higher mass loss OH/IR stars. We extend the VLBI SiO maser studies to OH/IR stars. The observations enable us to understand the SiO pumping mechanisms in higher mass loss evolved objects and compare those with Mira variables. Additionally, polarimetric observations of SiO masers help us to understand the magnetic field strength and morphology and to distinguish between conflicting polarization theories. The 43 GHz SiO maser observations of the OH/IR star OH 44.8-2.3 were performed with the VLBA in full polarization spectral line mode. Auxiliary EVLA observations were performed to allow for the absolute calibration of the polarization angle. The Zeeman splitting was measured by cross correlating the right and left circular polarization spectra as well as the S-curve fitting. Additionally, we analyzed the 1612 MHz OH maser observations of OH 44.8-2.3 from the VLA archive. The SiO masers of OH 44.8-2.2 form a ring located at ~5.4 AU around the star. The masers appear to be highly linearly polarized with fractional linear polarization up to 100%. The linear polarization vectors are consistent with a dipole field morphology in this star. We report a tentative detection of circular polarization of ~0.7% for the brightest maser feature. The magnetic field measured for this feature corresponds to 1.5\pm0.3 G. Additionally, the distribution of the 1612 MHz OH maser emission could indicate an elongated morphology.
In this notes we make a comparison between the arithmetic properties of irrational numbers and their dynamical properties under the Gauss map. We show some equivalences between different classifications of irrational numbers such as the Diophantine classes and numbers admitting approximations by rational numbers at a given 'speed'. We also show that irrational numbers with finite upper Lyapunov exponent for the Gauss map satisfy a Diophantine condition.
We discuss the resummation of the Goldstone boson contributions to the effective potential of the Minimal Supersymmetric Standard Model (MSSM). This eliminates the formal problems of spurious imaginary parts and logarithmic singularities in the minimization conditions when the tree-level Goldstone boson squared masses are negative or approach zero. The numerical impact of the resummation is shown to be almost always very small. We also show how to write the two-loop minimization conditions so that Goldstone boson squared masses do not appear at all, and so that they can be solved without iteration.
In this article is introduced and studied a set-indexed Markov property named C-Markov. This new definition fulfils one important expectation for a Markov property: there exists a natural set-indexed generalization of the concept of transition operator which leads to characterization and construction theorems for C-Markov processes. Several other usual Markovian notions, including Feller and strong Markov properties, can also be developed in this framework. Actually, the C-Markov property turns out to be a natural extension of the two-parameter \ast-Markov property to the multiparameter and as well the set-indexed settings. Moreover, generalizing a classic result of the real-parameter Markov theory, sample paths of multiparameter C-Feller processes are proved to be almost surely right-continuous. Concepts and results introduced in this study are illustrated with various examples.
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerged in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of its ability to measure material properties at atomic and electronic time scales and create excited states not accessible by the conventional means can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here, combining time-resolved femotosecond optical and resonant x-ray diffraction measurements on striped La1.75Sr0.25NiO4, we reveal unforeseen photo-induced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, unlike thermal phase fluctuations near the critical temperature in equilibrium10. Importantly, relaxation of the phase fluctuations are found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limit charge order recovery. This discovery of new aspect to phase fluctuation provides more holistic view for the importance of phase in ordering phenomena of quantum matter.
We report experimental and theoretical evidence that solid molecular ammonia becomes unstable at room temperature and high pressures and transforms into an ionic crystalline form. This material has been characterised in both hydrogenated NH3 and deuterated ND3 ammonia samples up to about 180 and 200 GPa, respectively, by infrared absorption, Raman spectroscopy and x-ray diffraction. The presence of a new, strong IR absorption band centered at 2500 cm-1 in NH3 (1900 cm-1 in ND3) signals the ionization of ammonia molecules into NH2- and NH4+ ions, in line with previous theoretical predictions. We find experimental evidence for a coexistence of two crystalline ionic forms, which our ab-initio structure searches predict to be the most stable at the relevant pressures. The ionic crystalline form of ammonia is stable at low temperatures, which contrasts with the behaviour of water in which no equivalent crystalline ionic phase has been found.
We consider $N=2$ supergravity coupled to $N=2$ Yang--Mills matter and discuss the nature of one--loop divergences. Using $N=1$ superfields and superspace methods, we describe the quantization of the system in the abelian case.
We propose a non-perturbative numerical approach to calculate the spectrum of a many-body Hamiltonian with time and momentum resolution by exactly recreating a scattering event using the time-dependent Schr\"odinger equation. Akin an actual inelastic scattering experiment, we explicitly account for the incident and scattered particles ( e.g. photons, neutrons, electrons...) in the Hamiltonian and obtain the spectrum by measuring the energy and momentum lost by the particle after interacting with the sample. We illustrate the method by calculating the spin excitations of a Mott-insulating Hubbard chain after a sudden quench with the aid of the time-dependent density matrix renormalization group (tDMRG) method. Our formalism can be applied to different forms of spectroscopies, such as neutron and Compton scattering, and electron energy-loss spectroscopy (EELS), for instance.
We analyse the properties of the Gogny interaction in homogeneous matter, with special emphasis on the isovector sector. We provide analytical expressions for both the single-particle and the bulk properties of symmetric and asymmetric nuclear matter. We perform an extensive analysis of these properties using 11 parametrizations extracted from the literature. We find that most Gogny interactions have low values for the slope of the symmetry energy, outside the range of empirically extracted values. As a test of extreme isospin dependence, we also study the mass-radius relations implied by the different Gogny equations of state. Our results call for a more careful fitting procedure of the isovector properties of Gogny functionals.
The conjecture that the elementary fermions are knotted flux tubes permit the construction of a phenomenology that is not accessible from the standard electroweak theory. In order to carry these ideas further we have attempted to formulate the elements of a field theory in which local SU(2) x U(1), the symmetry group of standard electroweak theory, is combined with global SU_q(2), the symmetry group of knotted solitons.
We study the behaviour of the spectrum of a family of one-dimensional operators with periodic high-contrast coefficients as the period goes to zero, which may represent e.g. the elastic or electromagnetic response of a two-component composite medium. Compared to the standard operators with moderate contrast, they exhibit a number of new effects due to the underlying non-uniform ellipticity of the family. The effective behaviour of such media in the vanishing period limit also differs notably from that of multi-dimensional models investigated thus far by other authors, due to the fact that neither component of the composite forms a connected set. We then discuss a modified problem, where the equation coefficient is set to a positive constant on an interval that is independent of the period. Formal asymptotic analysis and numerical tests with finite elements suggest the existence of localised eigenfunctions ("defect modes"), whose eigenvalues situated in the gaps of the limit spectrum for the unperturbed problem.
We review a generic structure of conventional (Nambu-Goto and Dirac-Born-Infeld-like) worldvolume actions for the superbranes and show how it is connected through a generalized action construction with a doubly supersymmetric geometrical approach to the description of super-p-brane dynamics as embedding world supersurfaces into target superspaces.
Donor spins in silicon are some of the most promising qubits for upcoming solid-state quantum technologies. The nuclear spins of phosphorus donors in enriched silicon have among the longest coherence times of any solid-state system as well as simultaneous qubit initialization, manipulation and readout fidelities near ~99.9%. Here we characterize the phosphorus in silicon system in the regime of "zero" magnetic field, where a singlet-triplet spin clock transition can be accessed, using laser spectroscopy and magnetic resonance methods. We show the system can be optically hyperpolarized and has ~10 s Hahn echo coherence times, even at Earth's magnetic field and below.
For a finite field $\mathbb{F}$, it is a basic result of Galois theory that the fixed field $E$ of $\text{Aut}(\mathbb{F}(x)/\mathbb{F})$ is a proper extension of $\mathbb{F}$. In this expository paper we construct, for all finite fields, an element $f\in \mathbb{F}(x)$ such that $E = \mathbb{F}(f)$. This element is shown to be easily computable in all cases using a simple formula. The approach is entirely elementary, and aimed at the student level; only a basic familiarity with Galois theory and field extensions is assumed.
The concept of Jeans gravitational instability is rediscussed in the framework of nonextensive statistics and its associated kinetic theory. A simple analytical formula generalizing the Jeans criterion is derived by assuming that the unperturbed self- gravitating collisionless gas is kinetically described by the $q$-parameterized class of power law velocity distributions. It is found that the critical values of wavelength and mass depend explicitly on the nonextensive $q$-parameter. The standard Jeans wavelength derived for a Maxwellian distribution is recovered in the limiting case $q$=1. For power-law distributions with cutoff, the instability condition is weakened with the system becoming unstable even for wavelengths of the disturbance smaller than the standard Jeans length $\lambda_J$.
Very-high-energy gamma-ray flares of TeV blazars are generally accompanied by simultaneous flaring activity in X-rays. The recent observations by the Whipple collaboration of an ``orphan'' TeV flare of 1ES 1959+650 (without simultaneous X-ray flare) is very hard to reconcile with the standard leptonic SSC model which is routinely very successfully employed to explain the SED and spectral variability of TeV blazars. In this paper, an alternative scenario is suggested in which the ``orphan'' TeV flare may originate from relativistic protons, interacting with an external photon field supplied by electron-synchrotron radiation reflected off a dilute reflector. While the external photons will be virtually ``invisible'' to the co-moving ultrarelativistic electrons in the jet due to Klein-Nishina effects, their Doppler boosted energy is high enough to excite the $\Delta$ resonance from relativistic protons with Lorentz factors of ~ 10^3 - 10^4. This model is capable of explaining the ``orphan'' TeV flare of 1ES 1959+650 with plausible parameters, thus constraining the number and characteristic energy of relativistic protons in the jet of this blazar.
The psu(2,2|4) integrable super spin chain underlying the AdS/CFT correspondence has integrable boundary states which describe set-ups where k D3-branes get dissolved in a probe D5-brane. Overlaps between Bethe eigenstates and these boundary states encode the one-point functions of conformal operators and are expressed in terms of the superdeterminant of the Gaudin matrix that in turn depends on the Dynkin diagram of the symmetry algebra. The different possible Dynkin diagrams of super Lie algebras are related via fermionic dualities and we determine how overlap formulae transform under these dualities. As an application we show how to consistently move between overlap formulae obtained for k=1 from different Dynkin diagrams.
We report electronic transmission properties of a tight binding Aharonov-Bohm ring threaded by a magnetic flux, to one arm of which a finite cluster of atoms has been attached from one side. we demonstrate that, by suitably choosing the number of scatterers in each arm of the quantum ring and, by decoupling the ring from the atomic cluster, the transmission across the ring can be completely blocked when the flux threading the ring becomes equal to half the fundamental flux quantum. A transmission resonance then occurs immediately as the coupling between the ring and the impurity cluster is switched 'on'. It is shown that the delta-like transmission resonances occur precisely at the eigenvalues of the side coupled chain of atoms.Thw 'switching' effect can be observed either for all the eigenvalues of the isolated atomic cluster, or for a selected set of them, depending on the number of scatterers in the arms of the ring. The ring-dot coupling can be gradually increased to suppress the oscillations in the magneto-transmission completely. However, the suppression can lead either to a complete transparency or no transmission at all, occasionally accompanied by a reversal of phase at special values of the magnetic flux.
We consider the random-phase sine-Gordon model in two dimensions. It describes two-dimensional elastic systems with random periodic disorder, such as pinned flux-line arrays, random field XY models, and surfaces of disordered crystals. The model exhibits a super-rough glass phase at low temperature $T<T_{c}$ with relative displacements growing with distance $r$ as $\bar{\langle [\theta(r)-\theta(0)]^2\rangle} \simeq A(\tau) \ln^2 (r/a)$, where $A(\tau) = 2 \tau^2- 2 \tau^3 +\mathcal{O}(\tau^4)$ near the transition and $\tau=1-T/T_{c}$. We calculate all higher cumulants and show that they grow as $\bar{\langle[\theta(r)-\theta(0)]^{2n}\rangle}_c \simeq [2 (-1)^{n+1} (2n)! \zeta(2n-1) \tau^2 + \mathcal{O}(\tau^3) ] \ln(r/a)$, $n \geq 2$, where $\zeta$ is the Riemann zeta function. By summation, we obtain the decay of the exponential correlation function as $\bar{\langle e^{iq\left[\theta(r)-\theta(0)\right]}\rangle} \simeq (a/r)^{\eta(q)} \exp\boldsymbol(-\frac{1}{2}\mathcal{A}(q)\ln^2(r/a)\boldsymbol)$ where $\eta(q)$ and ${\cal A}(q)$ are obtained for arbitrary $q \leq 1$ to leading order in $\tau$. The anomalous exponent is $\eta(q) = c q^2 - \tau^2 q^2 [2\gamma_E+\psi(q)+\psi(-q)]$ in terms of the digamma function $\psi$, where $c$ is non-universal and $\gamma_E$ is the Euler constant. The correlation function shows a faster decay at $q=1$, corresponding to fermion operators in the dual picture, which should be visible in Bragg scattering experiments.
The Omega-Omega (SIJ=-6,0,0) dibaryon state is studied with the extended quark-delocalization color-screening model including a pi meson exchange tail, which reproduces the properties of the deuteron quantitatively. We find the mass of the di-Omega to be about 45 MeV lower than the Omega-Omega threshold. The effect of channel coupling due to the tensor force has been calculated and found to be small in this case. We have also studied the effect of other pseudoscalar meson exchanges and sensitivity to the short-range cutoff radius, r_0, for the meson exchanges.
The muon anomalous magnetic dipole moment (MDM) is calculated in the framework of the minimal supersymmetric standard model (MSSM). In this paper, we discuss how the muon MDM depends on the parameters in MSSM in detail. We show that the contribution of the superparticle-loop becomes significant especially when $\tan\beta$ is large. Numerically, it becomes $O(10^{-8}-10^{-9})$ in a wide parameter space, which is within the reach of the new Brookhaven E821 experiment.
High-throughput atomistic simulations reveal the unique effect of solute atoms on twin variant selection in Mg-Al alloys. Twin embryos first undergo a stochastic incubation stage when embryos choose which twin variant to adopt, and then a deterministic growth stage when embryos expand without changing the selected twin variant. An increase in Al composition promotes the stochastic incubation behavior on the atomic level due to nucleation and pinning of interfacial disconnections. At compositions above a critical value, disconnection pinning results in multiple twin variant selection.
Topological edge-reconstruction occurs in hole-conjugate states of the fractional quantum Hall effect. The frequently studied polarized state of filling factor v=2/3 was originally proposed to harbor two counter-propagating edge modes: a downstream v=1 and an upstream v=1/3. However, charge equilibration between these two modes always led to an observed downstream v=2/3 charge mode accompanied by an upstream neutral mode (preventing an observation of the original proposal). Here, we present a new approach to synthetize the v=2/3 edge mode from its basic counter-propagating charged constituents, allowing a controlled equilibration between the two counter-propagating charge modes. This novel platform is based on a carefully designed double-quantum-well, which hosts two populated electronic sub-bands (lower and upper), with corresponding filling factors, vl & vu. By separating the 2D plane to two gated intersecting halves, each with different fillings, counter-propagating chiral modes can be formed along the intersection line. Equilibration between these modes can be controlled with the top gates' voltage and the magnetic field. Our measurements of the two-terminal conductance G2T and the presence of a neutral mode allowed following the transition from the non-equilibrated charged modes, manifested by G2T=(4/3)e2/h, to the fully equilibrated modes, with a downstream charge mode with G2T=(2/3)e2/h accompanied by an upstream neutral mode.
This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman's coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to the haplotype structure and a slower than expected decay of genetic correlation with distance revealed by recent studies of the human genome.