ShantanuT01/DACTYL-Pretraining huggingface dataset:
We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities in $\mathbb{R}^{2+1}$. We want to establish the small data global existence result, and in addition, we also demonstrate the pointwise asymptotic behaviour of the solution to the coupled system. The initial data are not required to have compact support, and this is achieved by applying the Alinhac's ghost weight method to both the wave and the Klein-Gordon equations.
Mesoscopic quantum phase coherence is important because it improves the prospects for handling quantum degrees of freedom in technology. Here we show that the development of such coherence can be monitored using magnetic neutron scattering from a one-dimensional spin chain Y2BaNiO5, a quantum spin fluid where no classical, static magnetic order is present. In the cleanest samples, the quantum coherence length is 20 nm, almost an order of magnitude larger than the classical antiferromagnetic correlation length of 3 nm. We also demonstrate that the coherence length can be modified by static and thermally activated defects in a quantitatively predictable manner.
A model of a stasis chamber, slowing the passage of time in its interior down to arbitrarily small rates relative to the outside world, is considered within classical general relativity. Since the model is adapted from the Majumdar-Papapetrou spacetime, interior spatial volumes are expanded by the same factor (cubed) as the rate of time is reduced. Real and apparent (gravitational) forces as perceived by an interior observer are altered, but in opposite ways. Comparison with special-relativistic time dilation shows the use of such a static stasis chamber to be economical only when the most drastic slowing of time relative to the outside world is desired (d(tau)/dt < 10^{-20}) or when one wants to avoid spending the time needed to accelerate to relativistic speeds.
We give a dual representation of minimal supersolutions of BSDEs with non-bounded, but integrable terminal conditions and under weak requirements on the generator which is allowed to depend on the value process of the equation. Conversely, we show that any dynamic risk measure satisfying such a dual representation stems from a BSDE. We also give a condition under which a supersolution of a BSDE is even a solution.
Given a local noetherian ring $R$ whose formal completion is integral, we introduce and study the $p$-radical closure $R^\text{prc}$. Roughly speaking, this is the largest purely inseparable $R$-subalgebra inside the formal completion $\hat{R}$. It turns out that the finitely generated intermediate rings $R\subset A\subset R^\text{prc}$ have rather peculiar properties. They can be used in a systematic way to provide examples of integral local rings whose normalization is non-finite, that do not admit a resolution of singularities, and whose formal completion is non-reduced.
This study of 117 low-redshift Im and Sm galaxies investigates the star formation rates of late-type galaxies, to determine whether they are quasi-continuous or dominated by bursts with quiescent interludes. We analyse the distribution of star formation timescales (stellar masses/star formation rates) for the entire sample, and of gas depletion timescales for those galaxies with gas mass measurements. We find that, on average, the late-type galaxies studied could have produced their total stellar masses by an extrapolation of their current star formation activity over a period of just under a Hubble time. This is not the case for a comparison sample of earlier-type galaxies, even those with disk-dominated morphologies and similar total stellar masses to the late-type galaxies. The earlier-type galaxies are on average forming their stars more slowly at present than the average rate over their past histories. No totally quiescent Im or Sm galaxies are found, and although some evidence of intrinsic variation in the star formation rate with time is found, this is typically less than a factor of 2 increase or decrease relative to the mean level. The Im and Sm galaxies have extensive gas reservoirs and can maintain star formation at the current rate for more than another Hubble time. The average spatial distribution of star formation in the Im galaxies, and to a lesser extent the Sm galaxies, is very similar to that of the older stellar population traced by the red light.
[abridged] Unbound young stellar systems, the loose ensembles of physically related young bright stars, trace the typical regions of recent star formation in galaxies. Their morphologies vary from small associations of stars to enormous stellar complexes. Being associated with star-forming regions of various sizes, they trace the regions where stars form at various scales, from compact clusters to whole galactic disks. They have been, thus, the focus of several studies with special interest on their demographics, classification, and structural morphology. Their surveys demonstrate that the clear distinction of these systems into well-defined classes is not straightforward, due to their low densities, asymmetric shapes and variety in structural parameters. Unbound stellar structures follow a hierarchical clustering pattern up to the scale of a whole star-forming galaxy. This structural pattern, which is usually characterized as self-similar or fractal, appears to be identical to that of star-forming giant molecular clouds and interstellar gas, driven mainly by turbulence cascade. In this short review, I make a concise compilation of our understanding of unbound young stellar systems across various environments in the local universe, as it is developed during the last 60 years. I present a factual assessment of the clustering behavior of star formation, as revealed from the assembling pattern of stars across loose stellar structures and its relation to the interstellar medium and the environmental conditions. I also provide a consistent account of the processes that possibly play important role in the formation of unbound stellar systems, compiled from both theoretical and observational investigations on the field.
Theoretical calculations of the structure, formation and migration of kinks on a non-dissociated screw dislocation in silicon have been carried out using density functional theory calculations as well as calculations based on interatomic potential functions. The results show that the structure of a single kink is characterized by a narrow core and highly stretched bonds between some of the atoms. The formation energy of a single kink ranges from 0.9 to 1.36 eV, and is of the same order as that for kinks on partial dislocations. However, the kinks migrate almost freely along the line of an undissociated dislocation unlike what is found for partial dislocations. The effect of stress has also been investigated in order to compare with previous silicon deformation experiments which have been carried out at low temperature and high stress. The energy barrier associated with the formation of a stable kink pair becomes as low as 0.65 eV for an applied stress on the order of 1 GPa, indicating that displacements of screw dislocations likely occur via thermally activated formation of kink pairs at room temperature.
We study the cold gas and dust properties for a sample of red star forming galaxies called "red misfits." We collect single-dish CO observations and HI observations from representative samples of low-redshift galaxies, as well as our own JCMT CO observations of red misfits. We also obtain SCUBA-2 850 um observations for a subset of these galaxies. With these data we compare the molecular gas, total cold gas, and dust properties of red misfits against those of their blue counterparts ("blue actives") taking non-detections into account using a survival analysis technique. We compare these properties at fixed position in the log SFR-log M* plane, as well as versus offset from the star-forming main sequence. Compared to blue actives, red misfits have slightly longer molecular gas depletion times, similar total gas depletion times, significantly lower molecular- and total-gas mass fractions, lower dust-to-stellar mass ratios, similar dust-to-gas ratios, and a significantly flatter slope in the $\log M_\mathrm{mol}$-$\log M_\star$ plane. Our results suggest that red misfits as a population are likely quenching due to a shortage in gas supply.
We determine sufficient conditions for the occurrence of a pointwise gradient estimate for the evolution operators associated to nonautonomous second order parabolic operators with (possibly) unbounded coefficients. Moreover we exhibit a class of operators which satisfy our conditions.
We present a unitary and gauge-invariant model with coupled channels, which provides a consistent description of pion photoproduction off nucleons in the E$_{0+}$ channel and eta-meson photoproduction off protons and deuterons. An effective field theory with hadrons and photons is constructed, which includes non-resonant Born terms as well as the S$_{11}$(1535) and S$_{11}$(1650) baryon resonances. Due to the coupling between the channels, the production of eta-mesons is strongly affected by the S$_{11}$(1650) although its direct coupling to the $\eta$N channel is negligible. The rho- and omega-meson exchange terms are important for achieving a consistent description of both pion- and photon-induced reactions.
We present the results of a preliminary H-alpha survey of M81 for novae conducted over a 5 month interval using the 5' field of view camera (WFCAM) on the Calypso Telescope at Kitt Peak, AZ. We observed M81 nearly every clear night during this interval, covering the entire galaxy, and discovered 12 novae. Our comprehensive time coverage allowed us to produce the most complete set of H-alpha light curves for novae in M81 to date. A raw nova rate for M81 gives 23 yr^-1 which, because of the nature of our survey, is a hard lower limit. An analysis of the completeness in our survey gives a corrected nova rate of 30 yr^-1. This agrees well with the rate of 33 (+13,-8) yr^-1, derived from Monte Carlo simulations using nova light curves and survey frame limits. The spatial distribution of the novae we discovered follows the bulge light much better than the disk or total light according to Kolmogorov - Smirnov tests of their radial distributions. The asymmetry in the distribution of novae across the major axis line of M81 implies a bulge-to-disk nova ratio of > 9 and supports the idea that novae originate primarily in older stellar populations.
English : In this article we associate to $G$, a truncated $p$-divisible $\mathcal O$-module of given signature, where $\mathcal O$ is a finite unramified extension of $\mathbb{Z}_p$, a filtration of $G$ by sub-$\mathcal O$-modules under the conditions that his Hasse $\mu$-invariant is smaller than an explicite bound. This filtration generalise the one given when $G$ is $\mu$-ordinary. The construction of the filtration relies on a precise study of the cristalline periods of a $p$-divisible $\mathcal O$-module. We then apply this result to families of such groups, in particular to stricts neighbourhoods of the $\mu$-ordinary locus inside some PEL Shimura varieties.   Fran\c{c}ais : Dans cet article, \`a $G$ un groupe $p$-divisible tronqu\'e muni d'une action d'une extension finie non ramifi\'ee $\mathcal O$ de $\mathbb{Z}_p$, et de signature donn\'ee, on associe sous une condition explicite sur son $\mu$-invariant de Hasse, une filtration de $G$ par des sous-$\mathcal O$-modules qui \'etend la filtration canonique lorsque $G$ est $\mu$-ordinaire. La construction se fait en \'etudiant les p\'eriodes cristallines des groupes $p$-divisibles avec action de $\mathcal O$. On applique ensuite cela aux familles de tels groupes, en particulier des voisinages stricts du lieu $\mu$-ordinaire dans des vari\'et\'es de Shimura PEL.
Stochastic processes time-changed by an inverse subordinator have been suggested as a way to model the price of assets in illiquid markets, where the jumps of the subordinator correspond to periods of time where one is unable to sell an asset. We develop an excursion theory for time-changed reflected Brownian motion and use this to express the price of certain European options with Parisian barrier condition in terms of solutions of a time-fractional PDE. We provide a general description of the occupation measures of time-changed processes and use this to prove a Ray-Knight theorem for the occupation measure of a time-changed Brownian motion with negative drift. We also show that the duration of the excursions on finite time intervals obey a Poisson-Dirichlet distribution when a reflected Brownian motion is time-changed by an inverse stable subordinator.
The general relativistic version is developed for Robertson's discussion of the Poynting-Robertson effect that he based on special relativity and Newtonian gravity for point radiation sources like stars. The general relativistic model uses a test radiation field of photons in outward radial motion with zero angular momentum in the equatorial plane of the exterior Schwarzschild or Kerr spacetime.
It is shown, that a spectrum generating algebras and wave functions for the integral and fractional quantum Hall effect are related by the non-unitary similarity transformation. This transformation corresponds to the introduction of the complex Chern-Simons gauge fields, in terms of which the second quantized form of FQHE can be developed
Transient {\it time-domain resonances} found recently in time-dependent solutions to Schr\"{o}dinger's equation are used to investigate the issue of the tunneling time in rectangular potential barriers. In general, a time frequency analysis shows that these transients have frequencies above the cutoff frequency associated with the barrier height, and hence correspond to non-tunneling processes. We find, however, a regime characterized by the barrier opacity, where the peak maximum $t_{max}$ of the {\it time-domain resonance} corresponds to under-the-barrier tunneling. We argue that $t_{max}$ represents the relevant tunneling time scale through the classically forbidden region.
The width of the giant dipole resonance (GDR) at finite temperature T in Sn-120 is calculated within the Phonon Damping Model including the neutron thermal pairing gap determined from the modified BCS theory. It is shown that the effect of thermal pairing causes a smaller GDR width at T below 2 MeV as compared to the one obtained neglecting pairing. This improves significantly the agreement between theory and experiment including the most recent data point at T = 1 MeV.
The temperature of hot accretion flows around black holes is sufficiently high for the ignition of nuclear reactions. This is potentially an important nucleosynthesis mechanism in the universe. As the first step in studying this problem, we need to measure physical quantities such as density and temperature of the accretion flow. In usual studies of the hot accretion flow, viscous dissipation is considered to be the only heating mechanism, while the heating caused by nuclear reactions is not considered. In this paper, we investigate whether the energy generation rate of nuclear reaction is important compared to the viscous heating. Our calculation indicates that the former is at most one percent of the latter and thus is not important. The dynamics of accretion flow can be therefore calculated in the usual way, without the need to consider heating due to nuclear reactions.
Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [googlemachine,gambetta2015building], and several-hundred-qubit machines are around the corner. Machines of this scale have the capacity to demonstrate quantum supremacy, the tipping point where QC is faster than the fastest classical alternative for a particular problem. Because error correction techniques will be central to QC and will be the most expensive component of quantum computation, choosing the lowest-overhead error correction scheme is critical to overall QC success. This paper evaluates two established quantum error correction codes---planar and double-defect surface codes---using a set of compilation, scheduling and network simulation tools. In considering scalable methods for optimizing both codes, we do so in the context of a full microarchitectural and compiler analysis. Contrary to previous predictions, we find that the simpler planar codes are sometimes more favorable for implementation on superconducting quantum computers, especially under conditions of high communication congestion.
Let $k$ be a field, with absolute Galois group $\Gamma$. Let $A/k$ be a finite \'etale group scheme of multiplicative type, i.e. a discrete $\Gamma$-module. Let $n \geq 2$ be an integer, and let $x \in H^n(k,A)$ be a cohomology class. We show that there exists a countable set $I$, and a familiy $(X_i)_{i \in I}$ of (smooth, geometrically integral) $k$-varieties, such that the following holds. For any field extension $l/k$, the restriction of $x$ vanishes in $H^n(l,A)$ if and only if (at least) one of the $X_i$'s has an $l$-point. We moreover show that the $X_i$'s can be made into an ind-variety. In the case $n=2$, we note that one variety is enough.
The ground state of the spin-Peierls system TiOCl was probed using synchrotron x-ray diffraction on a single-crystal sample at T = 6 K. We tracked the evolution of the structural superlattice peaks associated with the dimerized ground state as a function of pressure. The dimerization along the b axis is rapidly suppressed in the vicinity of a first-order structural phase transition at Pc = 13.1(1) GPa. The high-pressure phase is characterized by an incommensurate charge density wave perpendicular to the original spin chain direction. These results show that the electronic ground state undergoes a fundamental change in symmetry, indicating a significant change in the principal interactions.
Flare emissions in X-ray and EUV wavelengths have previously been modeled as the plasma response to impulsive heating from magnetic reconnection. Some flares exhibit gradually evolving X-ray and EUV light curves, which are believed to result from superposition of an extended sequence of impulsive heating events occurring in different adjacent loops or even unresolved threads within each loop. In this paper, we apply this approach to a long duration two-ribbon flare SOL2011-09-13T22 observed by the Atmosphere Imaging Assembly (AIA). We find that to reconcile with observed signatures of flare emission in multiple EUV wavelengths, each thread should be heated in two phases, an intense impulsive heating followed by a gradual, low-rate heating tail that is attenuated over 20-30 minutes. Each AIA resolved single loop may be composed of several such threads. The two-phase heating scenario is supported by modeling with both a zero-dimensional and a 1D hydrodynamic code. We discuss viable physical mechanisms for the two-phase heating in a post-reconnection thread.
A deeper understanding of video activities extends beyond recognition of underlying concepts such as actions and objects: constructing deep semantic representations requires reasoning about the semantic relationships among these concepts, often beyond what is directly observed in the data. To this end, we propose an energy minimization framework that leverages large-scale commonsense knowledge bases, such as ConceptNet, to provide contextual cues to establish semantic relationships among entities directly hypothesized from video signal. We mathematically express this using the language of Grenander's canonical pattern generator theory. We show that the use of prior encoded commonsense knowledge alleviate the need for large annotated training datasets and help tackle imbalance in training through prior knowledge. Using three different publicly available datasets - Charades, Microsoft Visual Description Corpus and Breakfast Actions datasets, we show that the proposed model can generate video interpretations whose quality is better than those reported by state-of-the-art approaches, which have substantial training needs. Through extensive experiments, we show that the use of commonsense knowledge from ConceptNet allows the proposed approach to handle various challenges such as training data imbalance, weak features, and complex semantic relationships and visual scenes.
Model calculations that include the effects of irreversible, environmental couplings on top of a coupled-channels dynamical description of the collision of two complex nuclei are presented. The Liouville-von Neumann equation for the time-evolution of the density matrix of a dissipative system is solved numerically providing a consistent transition from coherent to decoherent (and dissipative) dynamics during the collision. Quantum decoherence and dissipation are clearly manifested in the model calculations. Energy dissipation, due to the irreversible decay of giant-dipole vibrational states of the colliding nuclei, is shown to result in a hindrance of quantum tunneling and fusion.
N-body simulations and analytical calculations of the gravitational collapse in an expanding universe predict that halos should form with a diverging inner density profile, the cusp. There are some observational indications that the dark matter distribution in galaxies might be characterized by a finite core. This `core catastrophe' has prompted a search for alternatives to the CDM cosmogony. It is shown here that the discrepancy between theory and observations can be very naturally resolved within the standard CDM model, provided that gas is not initially smoothly distributed in the dark matter halo, but rather is concentrated in clumps of mass $\geq 0.01 %$ the total mass of the system. Dynamical friction acting on these lumps moving in the background of the dark matter particles, dissipates the clumps orbital energy and deposits it in the dark matter. Using Monte-Carlo simulations, it is shown that the dynamical friction provides a strong enough drag, and that with realistic baryonic mass fractions, the available orbital energy of the clumps is sufficient to heat the halo and turn the primordial cusp into a finite, non-diverging core --- overcoming the competing effect of adiabatic contraction due to gravitational influence of the shrinking baryonic component. Depending on the initial conditions, the total density distribution may either become more or less centrally concentrated. Possible consequences of the proposed mechanism for other problems in the CDM model and for the formation and early evolution of the baryonic component of galaxies are also briefly discussed.