ShantanuT01/DACTYL-Pretraining huggingface dataset:
We obtain existence and conormal Sobolev regularity of strong solutions to the 3D compressible isentropic Navier-Stokes system on the half-space with a Navier boundary condition, over a time that is uniform with respect to the viscosity parameters when these are small. These solutions then converge globally and strongly in $L^2$ towards the solution of the compressible isentropic Euler system when the viscosity parameters go to zero.
The characterization of the Intra-Cluster Medium (ICM) properties of high-redshift galaxy clusters is fundamental to our understanding of large-scale structure formation processes. We present the results of a multi-wavelength analysis of the very massive cluster MOO J1142$+$1527 at a redshift $z = 1.2$ discovered as part of the Massive and Distant Clusters of WISE Survey (MaDCoWS). This analysis is based on high angular resolution $Chandra$ X-ray and NIKA2 Sunyaev-Zel'dovich (SZ) data. Although the X-ray data have only about 1700 counts, we are able to determine the ICM thermodynamic radial profiles, namely temperature, entropy, and hydrostatic mass. These have been obtained with unprecedented precision at this redshift and up to $0.7R_{500}$, thanks to the combination of high-resolution X-ray and SZ data. The comparison between the galaxy distribution mapped in infrared by $Spitzer$ and the morphological properties of the ICM derived from the combined analysis of the $Chandra$ and NIKA2 data leads us to the conclusion that the cluster is an on-going merger. We measure the hydrostatic mass profile of the cluster in four angular sectors centered on the large-scale X-ray centroid. This allows us to estimate a systematic uncertainty on the cluster total mass that characterizes both the impact of the observed deviations from spherical symmetry and of the core dynamics on the mass profile. We further combine the X-ray and SZ data at the pixel level to obtain maps of the temperature and entropy distributions averaged along the line of sight. We find a relatively low entropy core at the position of the X-ray peak and high temperature regions located on its south and west sides. The increase in ICM temperature at the location of the SZ peak is expected given the merger dynamics. (abridged)
We consider the inhomogeneous nonlinear Schr\"odinger equation $$ i u_t +\Delta u+|x|^{-b}|u|^\alpha u = 0, $$ where $\frac{4-2b}{N}<\alpha<\frac{4-2b}{N-2}$ (when $N=2$, $\frac{4-2b}{N}<\alpha<\infty$) and $0<b<\min\{N/3,1\}$. For a radial initial data $u_0\in H^1(\mathbb{R}^N)$ under a certain smallness condition we prove that the corresponding solution is global and scatters. The smallness condition is related to the ground state solution of $-Q+\Delta Q+ |x|^{-b}|Q|^{\alpha}Q=0$ and the critical Sobolev index $s_c=\frac{N}{2}-\frac{2-b}{\alpha}$. This is an extension of the recent work \cite{paper2} by the same authors, where they consider the case $N=3$ and $\alpha=2$. The proof is inspired by the concentration-compactness/rigidity method developed by Kenig-Merle \cite{KENIG} to study $H^1(\mathbb{R}^N)$-critical problem and also Holmer-Roudenko \cite{HOLROU} in the case of $H^1(\mathbb{R}^N)$-subcritical equations.
In the first part of this work we consider an unstable non-BPS Dp-\bar{Dp}-brane pair in Type II superstring theory. Turning on a background NS-NS B-field (constant and nonzero along two spatial directions), we show that the tachyon responsible for the unstability has a complex GMS solitonic solution, which is interpreted as the low energy remnant of the resulting D(p-2)-brane. In the second part, we apply these results to construct the noncommutative soliton analogous of Witten's superconducting string. This is done by considering the complex GMS soliton arising from the D3-\bar{D3}-brane annihilation in Type IIB superstring theory. In the presence of left-handed fermions, we apply the Weyl-Wigner-Moyal correspondence and the bosonization technique to show that this object behaves like a superconducting wire.
The symmetric Anderson impurity model, with a soft-gap hybridization vanishing at the Fermi level with power law r > 0, is studied via the numerical renormalization group (NRG). Detailed comparison is made with predictions arising from the local moment approach (LMA), a recently developed many-body theory which is found to provide a remarkably successful description of the problem. Results for the `normal' (r = 0) impurity model are obtained as a specific case. Particular emphasis is given both to single-particle excitation dynamics, and to the transition between the strong coupling (SC) and local moment (LM) phases of the model. Scaling characteristics and asymptotic behaviour of the SC/LM phase boundaries are considered. Single-particle spectra are investigated in some detail, for the SC phase in particular. Here, the modified spectral functions are found to contain a generalized Kondo resonance that is ubiquitously pinned at the Fermi level; and which exhibits a characteristic low-energy Kondo scale that narrows progressively upon approach to the SC->LM transition, where it vanishes. Universal scaling of the spectra as the transition is approached thus results. The scaling spectrum characteristic of the normal Anderson model is recovered as a particular case, and is captured quantitatively by the LMA. In all cases the r-dependent scaling spectra are found to possess characteristic low-energy asymptotics, but to be dominated by generalized Doniach-Sunjic tails, in agreement with LMA predictions.
Upon reduction of the film thickness we observe a metal-insulator transition in epitaxially stabilized, spin-orbit coupled SrIrO$_3$ ultrathin films. By comparison of the experimental electronic dispersions with density functional theory at various levels of complexity we identify the leading microscopic mechanisms, i.e., a dimensionality-induced re-adjustment of octahedral rotations, magnetism, and electronic correlations. The astonishing resemblance of the band structure in the two-dimensional limit to that of bulk Sr$_2$IrO$_4$ opens new avenues to unconventional superconductivity by "clean" electron doping through electric field gating.
A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "macrostates" (e.g. sets of "microstates"), the consequence on the thermodynamic description of the system is studied in detail. When microstates within macrostates rapidly thermalize, the entire structure of the microscopic theory is recovered at the macrostate level. This is not the case when these microstates remain out of equilibrium leading to additional contributions to the entropy balance. Some of our results are illustrated for a model of two coupled quantum dots.
We present measurements of the two-dimensional genus of the SDSS-III BOSS catalogs to constrain cosmological parameters governing the shape of the matter power spectrum. The BOSS data are divided into twelve concentric shells over the redshift range $0.2 < z < 0.6$, and we extract the genus from the projected two-dimensional galaxy density fields. We compare the genus amplitudes to their Gaussian expectation values, exploiting the fact that this quantity is relatively insensitive to non-linear gravitational collapse. The genus amplitude provides a measure of the shape of the linear matter power spectrum, and is principally sensitive to $\Omega_{\rm c}h^{2}$ and scalar spectral index $n_{\rm s}$. A strong negative degeneracy between $\Omega_{\rm c}h^{2}$ and $n_{\rm s}$ is observed, as both can increase small scale power by shifting the peak and tilting the power spectrum respectively. We place a constraint on the particular combination $n_{\rm s}^{3/2} \Omega_{\rm c}h^{2}$ -- we find $n_{\rm s}^{3/2} \Omega_{\rm c}h^{2} = 0.1121 \pm 0.0043$ after combining the LOWZ and CMASS data sets, assuming a flat $\Lambda$CDM cosmology. This result is practically insensitive to reasonable variations of the power spectrum amplitude and linear galaxy bias. Our results are consistent with the Planck best fit $n_{\rm s}^{3/2}\Omega_{\rm c}h^{2} = 0.1139 \pm 0.0009$.
In this paper, we establish a new connection between Cox-Ingersoll-Ross (CIR) and reflected Ornstein-Uhlenbeck (ROU) models driven by either a standard Wiener process or a fractional Brownian motion with $H>\frac{1}{2}$. We prove that, with probability 1, the square root of the CIR process converges uniformly on compacts to the ROU process as the mean reversion parameter tends to either $\sigma^2/4$ (in the standard case) or to $0$ (in the fractional case). This also allows to obtain a new representation of the reflection function of the ROU as the limit of integral functionals of the CIR processes. The results of the paper are illustrated by simulations.
In this paper, we investigate abstract time-fractional evolution equations with nonlinear perturbations. We construct solutions of Lipschitz perturbation problems in arbitrary large time interval independent of the Lipschitz constants. We will extend well-known results for standard evolution equations such as the blow-up alternative, to the time-fractional evolution equations. We also prove the differentiability with respect to time of the solution when the perturbation is sufficiently smooth. The differentiability enables us to use the maximum principle. The theory on general Banach spaces enables us to deduce space regularity result easily.
We demonstrate that the interaction between excitons and a sea of incoherent electrons does not preclude excitons dressing by light. We investigate the role of exciton-electron scattering in the light dressing by measuring the dynamical absorption spectrum of a modulation-doped CdTe quantum well, which shows a clear evidence for significant electron scattering of the excitonic states. We show the occurrence of dressed and correlated excitons by detecting quantum coherent interferences through excitonic Autler-Townes doublet and ac Stark splitting, which evolves to Mollow triplet with gain. We also evidence the partial inhibition of the electron-exciton scattering by exciton-light coupling.
We measured the temperature dependences of the static magnetization and the spin excitation in a square-lattice multiferroics Ba$_2$MnGe$_2$O$_7$. An anisotropy gap of the observed low energy mode is scaled by electric polarization rather than a power of sublattice moment. Spin nematic interaction in effective spin Hamiltonian, which is equivalent to interaction of electric polarization, is responsible for the easy-axis anisotropy. The nontrivial behavior of the anisotropy gap can be rationalized as change of the hybridized $d$-$p$ orbital with temperature, leading to the temperature dependence of the spin nematic interaction.
We present results on the mass, spin, and redshift distributions with phenomenological population models using the ten binary black hole mergers detected in the first and second observing runs completed by Advanced LIGO and Advanced Virgo. We constrain properties of the binary black hole (BBH) mass spectrum using models with a range of parameterizations of the BBH mass and spin distributions. We find that the mass distribution of the more massive black hole in such binaries is well approximated by models with no more than 1% of black holes more massive than $45\,M_\odot$, and a power law index of $\alpha = {1.3}^{+1.4}_{-1.7}$ (90% credibility). We also show that BBHs are unlikely to be composed of black holes with large spins aligned to the orbital angular momentum. Modelling the evolution of the BBH merger rate with redshift, we show that it is at or increasing with redshift with 93% probability. Marginalizing over uncertainties in the BBH population, we find robust estimates of the BBH merger rate density of $R = {53.2}^{+55.8}_{-28.2}$ Gpc$^{-3}$ yr$^{-1}$ (90% credibility). As the BBH catalog grows in future observing runs, we expect that uncertainties in the population model parameters will shrink, potentially providing insights into the formation of black holes via supernovae, binary interactions of massive stars, stellar cluster dynamics, and the formation history of black holes across cosmic time.
The Fermi satellite has been reporting the detailed temporal properties of gamma-ray bursts (GRBs) in an extremely broad spectral range, 8 keV - 300 GeV, in particular, the unexpected delays of the GeV emission onsets behind the MeV emission of some GRBs. We focus on GRB 080916C, one of the Fermi-LAT GRBs for which the data of the delayed high-energy emission are quite extensive, and we show that the behavior of the high-energy emission of this burst can be explained by a model in which the prompt emission consists of two components: one is the MeV component due to the synchrotron-self-Compton radiation of electrons accelerated in the internal shock of the jet and the other is the high-energy component due to inverse Compton scattering of the photospheric X-ray emission of the expanding cocoon off the same electrons in the jet. Such an external inverse Compton effect could be important for other Fermi-LAT GRBs, including short GRBs as well. In this model, the delay timescale is directly linked to the physical properties of GRB progenitor.
In the paper, we consider the obstacle problem, with one and two irregular barriers, for semilinear evolution equation involving measure data and operator corresponding to a semi-Dirichlet form. We prove the existence and uniqueness of solutions under the assumption that the right-hand side of the equation is monotone and satisfies mild integrability conditions. To treat the case of irregular barriers, we extend the theory of precise versions of functions introduced by M. Pierre. We also give some applications to the so-called switching problem.
Taken together, the blank-field sub-mm surveys undertaken with SCUBA prior to the SHADES survey cover a total area of 460 sq. arcmin to a range of depths. However combining the results from these surveys has hitherto been complicated by the fact that different survey groups have used different methods of data reduction and source extraction. Here we present the results of re-reducing and analysing all of these blank field SCUBA in an almost identical manner to that employed in the SCUBA 8-mJy Survey. Comparative source catalogues are given which include a number of new significant source detections as well as failing to confirm some of those objects previously published. These new source catalogues have been combined to produce the most accurate number counts to date from 2 to 12.5 mJy. The cumulative number counts appear to steepen beyond S(850)=8mJy, which could indicate an intrinsic turn-over in the underlying luminosity function placing an upper limit on the luminosity (and hence mass) of a high redshift galaxy. We have also investigated the clustering properties of the bright SCUBA population by means of 2-point angular correlation functions. We find evidence for strong clustering broadly consistent with that measured for Extremely Red Objects (EROs). Nearest-neighbour analyses further support strong clustering on arcmin scales, rejecting the null hypothesis that the distribution of the bright submm sources is random at the 99% confidence level.
Let $f:S \fr B$ be a surface fibration with fibres of genus 5. We find a linear relation between the fundamental invariants of the surface. Namely $K_f^2=\chi_f+N$ where $N$ is the number of trigonal fibres. Our proof is based on the analysis of the relative canonical algebra $\cal{R}(f)$.
We present the results of our observations of the early stages of the 2012--2013 outburst of the transient black hole X-ray binary (BHXRB), Swift J1745$-$26, with the VLA, SMA, and JCMT (SCUBA--2). Our data mark the first multiple-band mm & sub-mm observations of a BHXRB. During our observations the system was in the hard accretion state producing a steady, compact jet. The unique combination of radio and mm/sub-mm data allows us to directly measure the spectral indices in and between the radio and mm/sub-mm regimes, including the first mm/sub-mm spectral index measured for a BHXRB. Spectral fitting revealed that both the mm (230 GHz) and sub-mm (350 GHz) measurements are consistent with extrapolations of an inverted power-law from contemporaneous radio data (1--30 GHz). This indicates that, as standard jet models predict, a power-law extending up to mm/sub-mm frequencies can adequately describe the spectrum, and suggests that the mechanism driving spectral inversion could be responsible for the high mm/sub-mm fluxes (compared to radio fluxes) observed in outbursting BHXRBs. While this power-law is also consistent with contemporaneous optical data, the optical data could arise from either jet emission with a jet spectral break frequency of $\nu_{{\rm break}}\gtrsim1\times10^{14}\,{\rm Hz}$ or the combination of jet emission with a lower jet spectral break frequency of $\nu_{{\rm break}}\gtrsim2\times10^{11}\,{\rm Hz}$ and accretion disc emission. Our analysis solidifies the importance of the mm/sub-mm regime in bridging the crucial gap between radio and IR frequencies in the jet spectrum, and justifies the need to explore this regime further.
We map the distribution and properties of the Milky Way's interstellar medium as traced by diffuse interstellar bands (DIBs) detected in near-infrared stellar spectra from the SDSS-III/APOGEE survey. Focusing exclusively on the strongest DIB in the H-band, at ~1.527 microns, we present a projected map of the DIB absorption field in the Galactic plane, using a set of about 60,000 sightlines that reach up to 15 kpc from the Sun and probe up to 30 magnitudes of visual extinction. The strength of this DIB is linearly correlated with dust reddening over three orders of magnitude in both DIB equivalent width (W_DIB) and extinction, with a power law index of 1.01 +/- 0.01, a mean relationship of W_DIB/A_V = 0.1 Angstrom mag^-1, and a dispersion of ~0.05 Angstrom mag^-1 at extinctions characteristic of the Galactic midplane. These properties establish this DIB as a powerful, independent probe of dust extinction over a wide range of A_V values. The subset of about 14,000 robustly detected DIB features have an exponential W_DIB distribution. We empirically determine the intrinsic rest wavelength of this transition to be lambda_0 = 15,272.42 Angstrom, and then calculate absolute radial velocities of the carrier, which display the kinematical signature of the rotating Galactic disk. We probe the DIB carrier distribution in three dimensions and show that it can be characterized by an exponential disk model with a scaleheight of about 100 pc and a scalelength of about 5 kpc. Finally, we show that the DIB distribution also traces large-scale Galactic structures, including the central long bar and the warp of the outer disk.
Magnets with frustration often show accidental degeneracies, characterized by a large classical ground-state space (CGSS). Quantum fluctuations may `select' one of these ground states -- a phenomenon labeled `order by (quantum) disorder' in literature. In this article, we examine the mechanism(s) by which such state selection takes place. We argue that a magnet, at low energies, maps to a particle moving on the CGSS. State selection corresponds to localization of the particle at a certain point on this space. We distinguish two mechanisms that can bring about localization. In the first, quantum fluctuations generate a potential on the CGSS. If the potential has a deep enough minimum, then the particle localizes in its vicinity. We denote this as `order by potential' (ObP). In the second scenario, the particle localizes at a self-intersection point due to bound-state formation -- a consequence of geometry and quantum interference. Following recent studies by the present authors, we denote this scenario as `order by singularity' (ObS). We place our discussion within the context of the one-dimensional spin-$S$ Kitaev model. We map out its CGSS which grows systematically with increasing system size. It resembles a network where the number of nodes increases exponentially. In addition, the number of wires that cross at each node also grows exponentially. This self-intersecting structure leads to ObS, with the low-energy physics determined by a small subset of the CGSS, consisting of `Cartesian' states. A contrasting picture emerges when an additional XY antiferromagnetic coupling is introduced. The CGSS simplifies dramatically, taking the form of a circle. Spin-wave fluctuations generate a potential on this space, giving rise to state selection by ObP under certain conditions. Apart from contrasting ObS and ObP, we discuss the possibility of ObS in macroscopic magnets.
Pulsar binaries, in particular redback systems, provide good sources to study the pulsar wind flow and its interaction with the companion stars. {\it Fermi}-LAT have proposed probable pulsar binary candidates in its catalogs. To identify pulsar binary sources from the catalog, orbital modulation search of binary candidates is an effective way. TESS observes in survey mode for a large part of the sky and thus provide an excellent data set to periodicity search of pulsar binary candidates by observing the flux variation, thought to mainly come from the stellar companion. Using TESS data we look for flux modulation of five pulsar binaries (or candidates) with reported orbital periods, including PSR J1023+0038, 3FGL J0523.3-2528, 3FGL J0212.1+5320, 3FGL J0744.1-2523 and PSR J1417-4402, demonstrating that TESS photometric data are very useful in identifying periodicities of redback-like systems. This method can be effective in searches for new pulsar binaries or similar binary systems in the future.
The J-matrix inverse scattering nucleon-nucleon potentials (JISP), describing both two-nucleon data and bound and resonant states of light nuclei to high accuracy, are tested on the total photoabsorption cross sections of Deuteron, Triton, 3He and 4He. The calculations in the three- and four-body systems are carried out via the Lorentz integral transform method and the hyperspherical harmonics (HH) technique. To this end the HH formalism has been adapted to accommodate non-local potentials. The cross sections calculated with the JISP are compared to those obtained with more traditional realistic interactions, which include two- and three-nucleon forces. While the results of the two kinds of potential models do not differ significantly at lower energies, beyond the resonance peak they show fairly large discrepancies, which increase with the nuclear mass. We argue that these discrepancies may be due to a probably incorrect long range behavior of the JISP, since the one pion exchange is not manifestly implemented there.
We consider transfer of a highly nonclassical quantum state through an optomechanical system. That is we investigate a protocol consisting of sequential upload, storage and reading out of the quantum state from a mechanical mode of an optomechanical system. We show that provided the input state is in a test-bed single-photon Fock state, the Wigner function of the recovered state can have negative values at the origin, which is a manifest of nonclassicality of the quantum state of the macroscopic mechanical mode and the overall transfer protocol itself. Moreover, we prove that the recovered state is quantum non-Gaussian for wide range of setup parameters. We verify that current electromechanical and optomechanical experiments can test this complete transfer of single photon.
In this paper, we completely characterize the niche graphs of bipartite tournaments and find their interesting properties.
We focus on the generating series for the rational special values of Pellarin's $L$-series in $1 \leq s \leq 2(q-1)$ indeterminates, and using interpolation polynomials we prove a closed form formula relating this generating series to the Carlitz exponential, the Anderson-Thakur function, and the Anderson generating functions for the Carlitz module. We draw several corollaries, including explicit formulae and recursive relations for Pellarin's $L$-series in the same range of $s$, and divisibility results on the numerators of the Bernoulli-Carlitz numbers by monic irreducibles of degrees one and two.