ShantanuT01/DACTYL-Pretraining huggingface dataset:
Fix an integer n>2 and let $(X(t))_{t\ge 0}$ be the pseudo-process driven by the high-order heat-type equation $\partial/\partial t=\pm\partial^N/\partial x^N$. The denomination "pseudo-process" means that $(X(t))_{t\ge 0}$ is related to a signed measure (which is not a probability measure) with total mass equal to 1. In this note, we present some results and discuss some problems concerning the pseudo-distributions of the first overshooting times of a single barrier $\{a\}$ or a double barrier $\{a,b\}$ by $(X(t))_{t\ge 0}$, as well as those of the sojourn times of $(X(t))_{t\ge 0}$ in the intervals $[a,+\infty)$ and $[a,b]$ up to a fixed time.
Magnetic skyrmions are particle-like chiral spin textures found in a magnetic film with out-of-planeanisotropy and are considered to be potential candidates as information carriers in next generationdata storage devices. Despite intense research into the nature of skyrmions and their dynamic prop-erties, there are several key challenges that still need to be addressed. In particular, the outstandingissues are the reproducible generation, stabilization and confinement of skyrmions at room tempera-ture. Here, we present a method for the capture of nanometer sized magnetic skyrmions in an arrayof magnetic topological defects in the form of an antidot lattice. With micromagnetic simulations,we elucidate the skyrmion formation in the antidot lattice and show that the capture is dependenton the antidot lattice parameters. This behavior is confirmed with scanning transmission x-ray mi-croscopy measurements. This demonstration that a magnetic antidot lattice can be implemented asa host to capture skyrmions provides a new platform for experimental investigations of skyrmionsand skyrmion based devices.
We demonstrate the collapse and revival features of the entanglement dynamics of different polarization-entangled photon states in a non-Markovian environment. Using an all-optical experimental setup, we show that entanglement can be revived even after it suffers from sudden death. A maximally revived state is shown to violate a Bell's inequality with 4.1 standard deviations which verifies its quantum nature. The revival phenomenon observed in this experiment provides an intriguing perspective on entanglement dynamics.
The recently discovered enhancement of eta photoproduction on the quasi-free neutron at energies around sqrt(s)~1.67 GeV is addressed within a SU(3) coupled channel model. The quasi-free cross sections on proton and neutron, sigma_n and sigma_p, can be quantitatively explained. In this study, the main source for the peak in sigma_n/sigma_p is a coupled channel effect in S-wave that explains the dip-bump structure in gamma n --> eta n. In particular, the photon coupling to the intermediate meson-baryon states is important. The stability of the result is extensively tested and consistency with several pion- and photon-induced reactions is ensured.
We study the effect of tachyon condensation on a brane antibrane pair in superstring theory separated in the transverse direction. The static properties of the tachyon potential analyzed using level truncated string field theory reproduces the desired property that the dependence of the minimum value of the potential on the initial distance of separation between the branes decreases as we include higher level terms. The rolling tachyon solution constructed using the conformal field theory methods shows that if the initial separation between the branes is less than a critical distance then the solution is described by an exactly marginal deformation of the original conformal field theory where the correlation functions of the deformed theory are determined completely in terms of the correlation functions of the undeformed theory without any need to regularize the theory. Using this we give an expression for the pressure on the brane-antibrane system as a power series expansion in \exp(C x^0) for an appropriate constant C.
We construct several novel examples of 3d $\mathcal{N}=2$ models whose free energy scales as $N^{3/2}$ at large $N$. This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d parents of the 3d models, matching the volume extracted from the $a$ conformal anomaly to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.
Statistics of hierarchical systems containing three or more stars are continuously improving. The Multiple Star Catalog (MSC) is currently the most comprehensive catalogue of multiple-star systems and contains component masses, orbital periods, and additional information. The systems in the MSC are interesting for several reasons, including the long-term dynamical evolution of few-body systems. Although the secular evolution of triples and quadruples has been explored before, a systematic study of the systems in the MSC including also quintuples and sextuples has not been carried out. Here, we explore the main-sequence (MS) evolution of stars from the MSC based on approximately 2x10^5 secular dynamical integrations. We estimate statistical probabilities for strong interactions during the MS such as tidal evolution and mass transfer, and the onset of dynamical instability. Depending on the assumed model for the unknown orbital elements, we find that the fraction of noninteracting systems is largest for triples (~0.9), and decreases to ~0.6-0.8 for sextuples. The fraction of strong interactions increases from ~0.1 to ~0.2 from triples to sextuples, and the fraction of dynamically unstable systems increases from ~0.001 to ~0.1-0.2. The larger fractions of strong interactions and dynamical instability in systems with increasing multiplicity can be attributed to increasingly complex secular evolution in these systems. Our results indicate that a significant fraction of high-multiplicity systems interact or become dynamically unstable already during the MS, with an increasing importance as the number of stars increases.
We investigate the nature of Ultra Faint dwarf spheroidal galaxies (UF dSphs) in a general cosmological context, simultaneously accounting for various "classical" dSphs and Milky Way (MW) properties, including their Metallicity Distribution Function (MDF). The model successfully reproduces both the observed [Fe/H]-Luminosity relation and the mean MDF of UFs. According to our results UFs are the living fossils of H2-cooling minihaloes formed at z>8.5, i.e. before the end of reionization. They are the oldest and the most dark matter-dominated (M/L > 100) dSphs in the MW system, with a total mass of M = 10^(7-8) Msun. The model allows to interpret the different shape of UFs and classical dSphs MDF, along with the frequency of extremely metal-poor stars in these objects. We discuss the "missing satellites problem" by comparing the UF star formation efficiencies with those derived for minihaloes in the Via Lactea simulation.
We present the first application of the recently developed Basis Light-Front Quantization (BLFQ) method to self-bound systems in quantum field theory, using the positronium system as a test case. Within the BLFQ framework, we develop a two-body effective interaction, operating only in the lowest Fock sector, that implements photon exchange, neglecting fermion self-energy effects. We then solve for the mass spectrum of this interaction at the unphysical coupling $\alpha=0.3$. The resulting spectrum is in good agreement with the expected Bohr spectrum of non-relativistic quantum mechanics. We examine in detail the dependence of the results on the regulators of the theory.
GRS 1915+105 being one of the brightest transient black hole binary (BHB) in the X-rays, offers a unique test-bed for the study of the connection between accretion and ejection mechanisms in BHBs. In particular, this source can be used to study the accretion disc wind and how it depends on the state changes in BHBs. Our aim is to investigate the origin and geometry of the accretion disc wind in GRS 1915+105. We analysed the spectra of GRS 1915+105 in the soft $\phi$ and hard $\chi$ classes, using the high resolution spectroscopy offered by Chandra HETGS. In the soft state, we find a series of wind absorption lines that follow a non linear dependence of velocity width, velocity shift and equivalent width with respect to ionisation, indicating a multiple component or stratified outflow. In the hard state we find only a faint Fe XXVI absorption line. We model the absorption lines in both the states using a dedicated MHD wind model to investigate a magnetic origin of the wind and to probe the cause of variability in the observed lines flux between the two states. The MHD disc wind model provides a good fit for both states, indicating the possibility of a magnetic origin of the wind. The multiple ionisation components of the wind are well characterised as a stratification of the same magnetic outflow. We find that the observed variability in the lines flux between soft and hard states cannot be explained by photo-ionisation alone but it is most likely due to a large (three orders of magnitude) increase in the wind density. We find the mass outflow rate of the wind to be comparable to the accretion rate, suggesting a intimate link between accretion and ejection processes that lead to state changes in BHBs.
Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, we prove for reasonably smooth solutions the optimal Strichartz estimates for pure gravity waves and the semi-classical Strichartz estimates for gravity-capillary waves; for both 2D and 3D waves. Here, by optimal we mean the gains of regularity (over the Sobolev embedding from Sobolev spaces to H\"older spaces) obtained for the linearized systems. Our proofs combine the paradifferential reductions of Alazard-Burq-Zuily with a dispersive estimate using a localized wave package type parametrix of Koch-Tataru.
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures and root-infidelity ones, to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we re-obtain the Landau--Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare novel uncertainty relations when using other known fidelity-based metrics.
In the first part of the paper, we give an explicit algorithm to compute the (genus zero) Gromov-Witten invariants of blow-ups of an arbitrary convex projective variety in some points if one knows the Gromov-Witten invariants of the original variety. In the second part, we specialize to blow-ups of P^r and show that many invariants of these blow-ups can be interpreted as numbers of rational curves on P^r having specified global multiplicities or tangent directions in the blown-up points. We give various numerical examples, including a new easy way to determine the famous multiplicity d^{-3} for d-fold coverings of rational curves on the quintic threefold, and, as an outlook, two examples of blow-ups along subvarieties, whose Gromov-Witten invariants lead to classical multisecant formulas.
We have compared the oxygen and nitrogen abundances derived from global emission-line SDSS spectra of galaxies using (1) the Te method and (2) two recent strong line calibrations: the ON and NS calibrations. Using the Te method, anomously high N/O abundances ratios have been found in some SDSS galaxies. To investigate this, we have Monte Carlo simulated the global spectra of composite nebulae by a mix of spectra of individual components, based on spectra of well-studied HII regions in nearby galaxies. We found that the Te method results in an underestimated oxygen abundance (and hence in an overestimated nitrogen-to-oxygen ratio) if HII regions with different physical properties contribute to the global spectrum of composite nebulae. This effect is somewhat similar to the small-scale temperature fluctuations in HII regions discussed by Peimbert. Our work thus suggests that the high Te-based N/O abundances ratios found in SDSS galaxies may not be real. However, such an effect is not expected to be present in dwarf galaxies since they have generally an uniform chemical composition. The ON and NS calibrations give O and N abundances in composite nebulae which agree with the mean luminosity-weighted abundances of their components to within 0.2 dex.
In the first two years since the launch of the Fermi Observatory, the Gamma-ray Burst Monitor (GBM) has detected over 500 Gamma-Ray Bursts (GRBs), of which 18 were confidently detected by the Large Area Telescope (LAT) above 100 MeV. Besides GRBs, GBM has triggered on other transient sources, such as Soft Gamma Repeaters (SGRs), Terrestrial Gamma-ray Flashes (TGFs) and solar flares. Here we present the science highlights of the GBM observations.
The initial and present-day mass functions (ICMF and PDMF, respectively) of the Galactic globular clusters (GCs) are constructed based on their observed luminosities, the stellar evolution and dynamical mass-loss processes, and the mass-to-light ratio (MLR). Under these conditions, a Schechter-like ICMF is evolved for approximately a Hubble time and converted into the luminosity function (LF), which requires finding the values of 5 free parameters: the mean GC age (\tA), the dissolution timescale of a $10^5 \ms$ cluster ($\tau_5$), the exponential truncation mass (\mc) and 2 MLR parametrising constants. This is achieved by minimising the residuals between the evolved and observed LFs, with the minimum residuals and realistic parameters obtained with MLRs that increase with luminosity (or mass). The optimum PMDFs indicate a total stellar mass of $\sim4\times10^7$ \ms\ still bound to GCs, representing $\sim15%$ of the mass in clusters at the beginning of the gas-free evolution. The corresponding ICMFs resemble the scale-free MFs of young clusters and molecular clouds observed in the local Universe, while the PDMFs follow closely a lognormal distribution with a turnover at $\mto\sim7\times10^4$\,\ms. For most of the GC mass range, we find an MLR lower than usually adopted, which explains the somewhat low \mto. Our results confirm that the MLR increases with cluster mass (or luminosity), and suggest that GCs and young clusters share a common origin in terms of physical processes related to formation.
An exact and general solution is presented for a previously open problem. We show that the superconformal R-symmetry of any 4d SCFT is exactly and uniquely determined by a maximization principle: it is the R-symmetry, among all possibilities, which (locally) maximizes the combination of 't Hooft anomalies a_{trial}(R) \equiv (9 Tr R^3-3 Tr R)/32. The maximal value of a_{trial} is then, by a result of Anselmi et. al., the central charge \it{a} of the SCFT. Our a_{trial} maximization principle almost immediately ensures that the central charge \it{a} decreases upon any RG flow, since relevant deformations force a_{trial} to be maximized over a subset of the previously possible R-symmetries. Using a_{trial} maximization, we find the exact superconformal R-symmetry (and thus the exact anomalous dimensions of all chiral operators) in a variety of previously mysterious 4d N=1 SCFTs. As a check, we verify that our exact results reproduce the perturbative anomalous dimensions in all perturbatively accessible RG fixed points. Our result implies that N =1 SCFTs are algebraic: the exact scaling dimensions of all chiral primary operators, and the central charges \it{a} and \it{c}, are always algebraic numbers.
Studies of the diffuse Galactic radio emission are interesting both for better understanding the physical conditions in our Galaxy and for minimising the contamination in cosmological measurements. Motivated by this we present Cosmic Background Imager 31 GHz observations of the Galactic regions NGC 6357, NGC 6334, W51 and W40 at $\sim$4$'$.5 resolution and conduct an investigation of the spectral emission process in the regions at 4$'$.5 and 1$^{\circ}$ resolution. We find that most of the emission in the regions is due to optically thin free-free. For 2 sub-regions of NGC 6334 and for a sub-region of W51 though, at 4$'$.5 resolution and at 31 GHz we detect less emission than expected from extrapolation of radio data at lower frequencies assuming a spectral index of $-$0.12 for optically thin free-free emission, at 3.3$\sigma$, 3.7$\sigma$ and 6.5$\sigma$ respectively. We also detect excess emission in a sub-region of NCG 6334 at 6.4$\sigma$, after ruling out any possible contribution from Ultra Compact HII (UCHII) regions. At 1$^{\circ}$ resolution we detect a spinning dust component in the Spectral Energy Distribution (SED) of W40 that accounts for 18$\pm$7 % of the total flux density in the region at the peak frequency of 37 GHz. Comparison with 100 ${\rm \mu m}$ data indicate an average dust emissivity for the sub-regions of $0.5\pm4.4$ $\mu$K(MJy sr$^{-1}$)$^{-1}$. Finally we translate the excess emission in the regions to an Anomalous Microwave Emission (AME) emissivity relative to the optical depth at 250 ${\rm \mu m }$. We find that this form of emissivity is independent of the AME significance and has a value somewhere in the order of 10$^4$ Jy.
Ytterbium-based delafossites with effective S=1/2 moments are investigated intensively as candidates for quantum spin-liquid ground states. While the synthesis of related cerium compounds has also been reported,many important details concerning their crystal, electronic, and magnetic structures are unclear. Here we analyze the S=1/2 system KCeO2, combining complementary theoretical methods. The lattice geometry was optimized and the band structure investigated using density functional theory extended to the level of a GGA+U calculation in order to reproduce the correct insulating behavior. The Ce 4f1 states were then analyzed in more detail with the help of ab initio wave-function-based computations. Unusually large effective crystal-field splittings of up to 320 meV are predicted, which puts KCeO2 in the strong field coupling regime. Our results reveal a subtle interplay between ligand-cage electrostatics and the trigonal field generated by the extended crystalline surroundings, relevant in the context of recent studies on tuning the nature of the ground-state wave function in 4f triangular-lattice and pyrochlore compounds. It also makes KCeO2 an interesting model system in relation to the effect of large crystal-field splittings on the anisotropy of intersite exchange in spin-orbit coupled quantum magnets.
The heat conducting compressible viscous flows are governed by the Navier-Stokes-Fourier (NSF) system. In this paper, we study the NSF system accomplished by the Newton law of cooling for the heat transfer at the boundary. On one part of the boundary, we consider the Navier slip boundary condition, while in the remaining part the inlet and outlet occur. The existence of a weak solution is proved via a new fixed point argument. With this new approach, the weak solvability is possible in Lipschitz domains, by making recourse to \(L^q\)-Neumann problems with \(q>n\).Thus, standard existence results can be applied to auxiliary problems and the claim follows by compactness techniques. Quantitative estimates are established.
We study the Brownian motion of a particle in a bounded circular 2-dimensional domain, in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it travels along the one-dimensional boundary. During the diffusion, the Brownian particle resets to its initial position with a constant rate $r$. The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.
We show that for sufficiently large $d$ and for $t\geq d+1$, there is a graph $G$ with average degree $(1-\varepsilon)\lambda t \sqrt{\ln d}$ such that almost every graph $H$ with $t$ vertices and average degree $d$ is not a minor of $G$, where $\lambda=0.63817\dots$ is an explicitly defined constant. This generalises analogous results for complete graphs by Thomason (2001) and for general dense graphs by Myers and Thomason (2005). It also shows that an upper bound for sparse graphs by Reed and Wood (2016) is best possible up to a constant factor.
With the discovery of the companions of 51 Peg, 55 Cnc, $\tau$ Boo, $\upsilon$ And, 70 Vir, 47 UMa, and Gl229, evolutionary and spectral models of gas giants and/or brown dwarfs with masses from 0.3 through 60 times that of Jupiter assume a new and central role in the emerging field of extrasolar planetary studies. In this contribution, we describe the structural, spectral, and evolutionary characteristics of such exotic objects, as determined by our recent theoretical calculations. These calculations can be used to establish direct search strategies via SIRTF, ISO, and HST (NICMOS), and via various ground-based adaptive optics and interferometric platforms planned for the near future.
Charged Higgs bosons are predicted in variety of theoretically well-motivated new physics models with extended Higgs sectors. In this study, we focus on a type-II two Higgs doublet model (2HDM-II) and consider a heavy charged Higgs with its mass ranging from 500 GeV to 1 TeV as dictated by the $b\to s\gamma$ constraints which render $M_{H^\pm}>480$ GeV. We study the dominant production mode $H^\pm t$ associated production with $H^\pm \to W^\pm A$ being the dominant decay channel when the pseudoscalar $A$ is considerably lighter. For such a heavy charged Higgs, both the decay products $W^\pm$ and $A$ are relatively boosted. In such a scenario, we apply the jet substructure analysis of tagging the fat pseudoscalar and $W$ jets in order to eliminate the standard model background efficiently. We perform a detailed detector simulation for the signal and background processes at the 14 TeV LHC. We introduce various kinematical cuts to determine the signal significance for a number of benchmark points with charged Higgs boson mass from 500 GeV to 1 TeV in the $W^\pm A$ decay channel. Finally we perform a multivariate analysis utilizing a boosted decision tree algorithm to optimize these significances.
Understanding the internal process of ConvNets is commonly done using visualization techniques. However, these techniques do not usually provide a tool for estimating the stability of a ConvNet against noise. In this paper, we show how to analyze a ConvNet in the frequency domain using a 4-dimensional visualization technique. Using the frequency domain analysis, we show the reason that a ConvNet might be sensitive to a very low magnitude additive noise. Our experiments on a few ConvNets trained on different datasets revealed that convolution kernels of a trained ConvNet usually pass most of the frequencies and they are not able to effectively eliminate the effect of high frequencies. Our next experiments shows that a convolution kernel which has a more concentrated frequency response could be more stable. Finally, we show that fine-tuning a ConvNet using a training set augmented with noisy images can produce more stable ConvNets.
We show that the non-commutative widths for flopping curves on smooth 3-folds introduced by Donovan-Wemyss are described by Katz's genus zero Gopakumar-Vafa invariants.