ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate a frustrated Ising spin system on the garnet lattice composed of a specific network of corner-sharing triangles. By means of Monte Carlo simulations with the heat bath algorithm, we discuss the magnetic properties at finite temperatures. It is shown that the garnet spin system with the nearest-neighbor couplings does not exhibit any magnetic transitions, yielding the large residual entropy at zero temperature. We also investigate the effect of the long-range dipolar interaction systematically to determine the phase diagram of the Ising model on the garnet lattice. We find that there appear a variety of distinct phases depending on the cutoff length of the long-range interaction, in contrast to the pyrochlore spin-ice systems.
Filamentary structures are ubiquitous in observations of real molecular clouds, and also in simulations of turbulent, self-gravitating gas. However, making comparisons between observations and simulations is complicated by the difficulty of estimating volume-densities observationally. Here, we have post-processed hydrodynamical simulations of a turbulent isothermal molecular cloud, using a full time-dependent chemical network. We have then run radiative transfer models to obtain synthetic line and continuum intensities that can be compared directly with those observed. We find that filaments have a characteristic width of $\,\sim\!0.1 \, {\rm pc}$, both on maps of their true surface density, and on maps of their $850 \, {\rm \mu m}$ dust-continuum emission, in agreement with previous work. On maps of line emission from CO isotopologues, the apparent widths of filaments are typically several times larger because the line intensities are poorly correlated with the surface density. On maps of line emission from dense-gas tracers such as N$_2$H$^+$ and HCN, the apparent widths of filaments are $\lesssim 0.1 \, {\rm pc}$. Thus, current observations of molecular-line emission are compatible with the universal $0.1 \, {\rm pc}$ filament width inferred from ${\it Herschel}$ observations, provided proper account is taken of abundance, optical-depth, and excitation considerations. We find evidence for $\sim 0.4 \, {\rm km \, s^{-1}}$ radial velocity differences across filaments. These radial velocity differences might be a useful indicator of the mechanism by which a filament has formed or is forming, for example the turbulent cloud scenario modelled here, as against other mechanisms such as cloud-cloud collisions.
We consider a fractional Laplace equation and we give a self-contained elementary exposition of the representation formula for the Green function on the ball. In this exposition, only elementary calculus techniques will be used, in particular, no probabilistic methods or computer assisted algebraic manipulations are needed. The main result in itself is not new, however we believe that the exposition is original and easy to follow, hence we hope that this paper will be accessible to a wide audience of young researchers and graduate students that want to approach the subject, and even to professors that would like to present a complete proof in a PhD or Master Degree course.
We present a study of certain singular one-parameter subfamilies of Calabi-Yau threefolds realized as anticanonical hypersurfaces or complete intersections in toric varieties. Our attention to these families is motivated by the Doran-Morgan classification of variations of Hodge structure which can underlie families of Calabi-Yau threefolds with $h^{2,1} = 1$ over the thrice-punctured sphere. We explore their torically induced fibrations by $M$-polarized K3 surfaces and use these fibrations to construct an explicit geometric transition between an anticanonical hypersurface and a nef complete intersection through a singular subfamily of hypersurfaces. Moreover, we show that another singular subfamily provides a geometric realization of the missing "14th case" variation of Hodge structure from the Doran-Morgan list.
Given a spherical spacelike three-geometry, there exists a very simple algebraic condition which tells us whether, and in which, Schwarzschild solution this geometry can be smoothly embedded. One can use this result to show that any given Schwarzschild solution covers a significant subset of spherical superspace and these subsets form a sequence of nested domains as the Schwarzschild mass increases. This also demonstrates that spherical data offer an immediate counter example to the thick sandwich `theorem'.
We consider the joint distribution of eigenvalue clusters of the Wigner ensemble separated by macroscopic distances (i.e., on the same scale as the difference between the edges of the semicircle law). We prove that under an averaging condition, the correlation function governing any finite collection of clusters converges to that of independence point processes. The proof relies heavily on the machinery developed by Erdos, Ramirez, Schlein, and Yau.
All cool stars with outer convective zones have the potential to exhibit stochastically excited stellar oscillations. In this work, we explore the outer layers of stars less massive than the Sun. In particular, we have computed a set of stellar models raging from 0.4 to 0.9 $M_\odot$ with the aim at determining the impact on stellar oscillations of two physical processes occurring in the envelopes of these stars. Namely, the partial ionisation of chemical elements and the electrostatic interactions between particles in the outer layers. We find that alongside with partial ionisation, Coulomb effects also impact the acoustic oscillation spectrum. We confirm the well-known result that as the mass of a star decreases, the electrostatic interactions between particles become relevant. We found that their impact on stellar oscillations increases with decreasing mass, and for the stars with the lowest masses ($M \lesssim 0.6 M_\odot$), it is shown that Coulomb effects dominate over partial ionisation processes producing a strong scatter on the acoustic modes. The influence of Coulomb interactions on the sound-speed gradient profile produces a strong oscillatory behaviour with diagnostic potential for the future.
Bi$_2$Te$_3$ is a topological insulator whose unique properties result from topological surface states in the band gap. The neutralization of scattered low energy Na$^+$, which is sensitive to dipoles that induce inhomogeneities in the local surface potential, is larger when scattered from Te than from Bi, indicating an upwards dipole at the Te sites and a downwards dipole above Bi. These dipoles are caused by the spatial distribution of the conductive electrons in the topological surface states. This result demonstrates how this alkali ion scattering method can be applied to provide direct experimental evidence of the spatial distribution of electrons in filled surface states.
Using as an illustrative example the p=1 operator-ordered Wheeler-DeWitt equation for a closed, radiation-filled Friedmann-Robertson-Walker universe, we introduce and discuss the supersymmetric double Darboux method in quantum cosmology. A one-parameter family of ``quantum'' universes and the corresponding ``wavefunctions of the universe" for this case are presented
Previous work on applications of Abstract Differential Geometry (ADG) to discrete Lorentzian quantum gravity is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantum causal sets involved therein, on which a finitary (:locally finite), singularity-free, background manifold independent and geometrically prequantized version of the gravitational vacuum Einstein field equations were seen to hold, into a topos structure. This topos is seen to be a finitary instance of both an elementary and a Grothendieck topos, generalizing in a differential geometric setting, as befits ADG, Sorkin's finitary substitutes of continuous spacetime topologies. The paper closes with a thorough discussion of four future routes we could take in order to further develop our topos-theoretic perspective on ADG-gravity along certain categorical trends in current quantum gravity research.
We consider a well known model for lipid-bilayer membrane vesicles exhibiting phase separation, incorporating a phase field with finite curvature elasticity. We prove the existence of a plethora of equilibria, corresponding to symmetry-breaking solutions of the Euler-Lagrange equations, via global bifurcation from the spherical state. To the best of our knowledge, this constitutes the first rigorous existence results for this class of problems. We overcome several difficulties in carrying this out. Due to inherent in-plane fluidity combined with finite curvature elasticity, neither the Eulerian (spatial) nor the Lagrangian (material) description of the model lends itself well to analysis. Instead we adopt a singularity-free radial-map description that effectively eliminates the grossly underdetermined in-plane fluid deformation. The resulting governing equations comprise a quasi-linear elliptic system with lower-order nonlinear constraints. We then show the equivalence of our problem to that of finding the zeros of compact vector field. The latter is not routine; we obtain certain spectral estimates and then shift the principle part of the operator. With this in hand, we combine well known group-theoretic ideas for symmetry-breaking with global bifurcation theory to obtain our results.
In the light of the recent LHC data on proton-proton and lead-lead collisions we examine the question of the multiplicity scaling of HBT radii in relativistic nuclei and particle interactions. Within the UrQMD transport approach we study a large variety of system sizes at different beam energies and extract the HBT radii. In the calculation, we find a good scaling of the radii as a function of charged particle multiplicity, if the change in the multiplicity is caused by a change of centrality at the same energy. However, the scaling is only approximate when the energy, $\sqrt{s}$, is changed and breaks down when comparing pp to AA reactions.
We introduce new tools for studying modular flow in AdS/CFT. These tools allow us to efficiently extract bulk information related to causality and locality. For example, we discuss the relation between analyticity in modular time and entanglement wedge nesting which can then be used to extract the location of the Ryu-Takayanagi (RT) surface directly from the boundary theory. Probing the RT surface close to the boundary our results reduce to the recent proof of the Quantum Null Energy Condition. We focus on heavy probe operators whose correlation functions are determined by spacelike geodesics. These geodesics interplay with the RT surface via a set of rules that we conjecture and give evidence for using the replica trick.
The MOST, CoRoT, and Kepler space missions led to the discovery of a large number of intriguing, and in some cases unique, objects among which are pulsating stars, stars hosting exoplanets, binaries, etc. Although the space missions deliver photometric data of unprecedented quality, these data are lacking any spectral information and we are still in need of ground-based spectroscopic and/or multicolour photometric follow-up observations for a solid interpretation. Both faintness of most of the observed stars and the required high S/N of spectroscopic data imply the need of using large telescopes, access to which is limited. In this paper, we look for an alternative, and aim for the development of a technique allowing to denoise the originally low S/N spectroscopic data, making observations of faint targets with small telescopes possible and effective. We present a generalization of the original Least-Squares Deconvolution (LSD) method by implementing a multicomponent average profile and a line strengths correction algorithm. The method was successfully tested on the high resolution spectra of Vega and a Kepler star, KIC04749989. Application to the two pulsating stars, 20 Cvn and HD189631, showed that the technique is also applicable to intrinsically variable stars: the results of frequency analysis and mode identification from the LSD model spectra for both objects are in good agreement with the findings from literature. Depending on S/N of the original data and spectral characteristics of a star, the gain in S/N in the LSD model spectrum typically ranges from 5 to 15 times. The restored LSD model spectra contain all the information on line profile variations present in the original spectra. The method is applicable to both high- (>30 000) and low- (<30 000) resolution spectra, though the information that can be extracted from the latter is limited by the resolving power itself.
We developed means to produce wafer scale, high-quality graphene films as large as 3 inch wafer size on Ni and Cu films under ambient-pressure and transfer them onto arbitrary substrates through instantaneous etching of metal layers. We also demonstrated the applications of the large-area graphene films for the batch fabrication of field-effect transistor (FET) arrays and stretchable strain gauges showing extraordinary performances. Transistors showed the hole and electron mobilities of the device of 1,100 cm2/Vs and 550 cm2/Vs at drain bias of -0.75V, respectively. The piezo-resistance gauge factor of strain sensor was ~6.1. These methods represent a significant step toward the realization of graphene devices in wafer scale as well as application in optoelectronics, flexible and stretchable electronics.
We report sub-arcsecond X-ray imaging spectroscopy of M87 and the core of the Virgo cluster with the Chandra X-ray Observatory. The X-ray morphology shows structure on arcsecond (~100 pc) to ten arcminute (~50 kpc) scales, the most prominent feature being an "arc" running from the east, across the central region of M87 and off to the southwest. A ridge in the radio map, ending in an "ear"-shaped structure, follows the arc to the east. Depressions in the X-ray surface brightness correspond to the inner radio lobes and there is no evidence of shock-heated gas surrounding them. There are also at least two approximately circular (centered near the nucleus) "edges" in the X-ray brightness distribution, the radii of which are slightly larger than the nuclear distances of the inner radio lobes and intermediate radio ridges, respectively. We speculate that these discontinuities may be spherical pulses or "fronts" driven by the same jet activity as is responsible for the radio structure; such pulses are found in recent numerical simulations. All these results provide good evidence that the nuclear activity affects the intra-cluster medium. We present a temperature map of the intra-cluster medium, and obtain the temperature, pressure and cooling time as a function of nuclear distance for the arcs and the ambient intra-cluster medium. We show that the gas in the arcs is cooler than, and probably over-pressured with respect to, the ambient intra-cluster medium. The metal abundances of the cooler gas in the arc are somewhat enhanced relative to the ambient intra-cluster medium, favoring a ``buoyant plume'' origin for the X-ray arc, in which ambient gas near the nucleus is entrained by buoyant radio plasma and carried to larger nuclear distances. (Abstract truncated).
(abridged) This paper aims at deciphering the dynamics of the envelope of a rotating star when some angular momentum loss due to mass loss is present. We especially wish to know when the spin-down flow forced by the mass loss supersedes the baroclinic flows that pervade the radiative envelope of rotating stars. We consider a Boussinesq fluid enclosed in a rigid sphere whose flows are forced both by the baroclinic torque, the spin-down of an outer layer, and an outward mass flux. The spin-down forcing is idealized in two ways: either by a rigid layer that imposes its spinning down velocity at some interface or by a turbulent layer that imposes a stress at this same interface to the interior of the star. In the case where the layer is rigid and imposes its velocity, we find that, as the mass-loss rate increases, the flow inside the star shows two transitions: the meridional circulation associated with baroclinic flows is first replaced by its spin-down counterpart, while at much stronger mass-loss rates the baroclinic differential rotation is superseded by the spin-down differential rotation. In fact, we find three wind regimes: weak (or no wind), moderate, and strong. In the first case, the flow in the radiative envelope is of baroclinic origin. In the moderate case, the circulation results from the spin-down while the differential rotation may either be of baroclinic or of spin-down origin, depending on the coupling between mass and angular momentum losses. For fast rotating stars, our model says that the moderate wind regime starts when mass loss is higher than ~1e-11 Msun/yr. In the strong wind case, the flow in the radiative envelope is mainly driven by angular momentum advection. This latter transition depends on the mass and the rotation rate of the star, being around 1e-8 Msun/yr for a 3 Msun ZAMS star rotating at 200 km/s according to our model.
We give a formula for the number of genus-two fixed-complex-structure degree-d plane curves passing through 3d-2 points in general position. This is achieved by completing Katz-Qin-Ruan's approach. This paper's formula agrees with the one obtained by the author in a completely different way.
For both localized and periodic initial data, we prove local existence in classical energy space $H^s, s>\frac{3}{2}$, for a class of dispersive equations $u_{t}+(n(u))_{x}+Lu_{x}=0$ with nonlinearities of mild regularity. Our results are valid for symmetric Fourier multiplier operators $L$ whose symbol is of temperate growth, and $n(\cdot)$ in local Sobolev space $H^{s+2}_{\mathrm{loc}}(\mathbb{R})$. In particular, the results include non-smooth and exponentially growing nonlinearities. Our proof is based on a combination of semi-group methods and a new composition result for Besov spaces. In particular, we extend a previous result for Nemytskii operators on Besov spaces on $\mathbb{R}$ to the periodic setting by using the difference-derivative characterization of Besov spaces.
Total-Routhian-Surface calculations have been performed to investigate the shape evolutions of $A\sim80$ nuclei, $^{80-84}$Zr, $^{76-80}$Sr and $^{84,86}$Mo. Shape coexistences of spherical, prolate and oblate deformations have been found in these nuclei. Particularly for the nuclei, $^{80}$Sr and $^{82}$Zr, the energy differences between two shape-coexisting states are less than 220 keV. At high spins, the $g_{9/2}$ shell plays an important role for shape evolutions. It has been found that the alignment of the $g_{9/2}$ quasi-particles drives nuclei to be triaxial.
We have previously focused on studying the electron-capture isotopes within the dynamic spiral-arms model and empirically derived the energy dependence of the electron attachment rate using the observation of $^{49}$Ti/$^{49}$V and $^{51}$V/$^{51}$Cr ratios in cosmic rays (Benyamin et al. 2017). We have also shown how this relation recovers the energy dependence seen in the lab measurements (Letaw et al. 1985). In this work we use this relation to construct the $^{44}$Ca/$^{44}$Ti ratio and place a lower limit on the amount of $^{44}$Ti that is required to be nucleosynthesized at the source. The results also imply that the acceleration process of the radioisotopes cannot be much longer than a century time scale (or else the required nucleosynthesized amount has to be correspondingly larger). We also provide a similar lower limit on the source $^{60}$Fe by comparing to the recently observed $^{60}$Fe/$^{56}$Fe (Binns et al. 2016).
Event cameras are considered to have great potential for computer vision and robotics applications because of their high temporal resolution and low power consumption characteristics. However, the event stream output from event cameras has asynchronous, sparse characteristics that existing computer vision algorithms cannot handle. Spiking neural network is a novel event-based computational paradigm that is considered to be well suited for processing event camera tasks. However, direct training of deep SNNs suffers from degradation problems. This work addresses these problems by proposing a spiking neural network architecture with a novel residual block designed and multi-dimension attention modules combined, focusing on the problem of depth prediction. In addition, a novel event stream representation method is explicitly proposed for SNNs. This model outperforms previous ANN networks of the same size on the MVSEC dataset and shows great computational efficiency.
To investigate the possible cooling of the corona by soft X-rays bursts, we have studied 114 bursts embedded in the known X-ray evolution of 4U 1636-536. We have grouped these bursts according to the ratio of the flux in the 1.5--12 keV band with respect to that in the 15--50 keV band, as monitored by RXTE/ASM and Swift/BAT, respectively. We have detected a shortage at hard X-rays while bursting. This provides hints for a corona cooling process driven by soft X-rays fed by the bursts that occurred on the surface of neutron star. The flux shortage at 30--50 keV has a time lag of 2.4$\pm$1.5 seconds with respect to that at 2--10 keV, which is comparable to that of 0.7$\pm$0.5 seconds reported in bursts of IGR 17473-2721. We comment on the possible origin of these phenomena and on the implications for the models on the location of the corona.
Reaction-diffusion PDEs and particle-based stochastic reaction-diffusion (PBSRD) models are commonly-used approaches for modeling the spatial dynamics of chemical and biological systems. Standard reaction-diffusion PDE models ignore the underlying stochasticity of spatial transport and reactions, and are often described as appropriate in regimes where there are large numbers of particles in a system. Recent studies have proven the rigorous large-population limit of PBSRD models, showing the resulting mean-field models (MFM) correspond to non-local systems of partial-integro differential equations. In this work we explore the rigorous relationship between standard reaction-diffusion PDE models and the derived MFM. We prove that the former can be interpreted as an asymptotic approximation to the later in the limit that bimolecular reaction kernels are short-range and averaging. As the reactive interaction length scale approaches zero, we prove the MFMs converge at second order to standard reaction-diffusion PDE models. In proving this result we also establish local well-posedness of the MFM model in time for general systems, and global well-posedness for specific reaction systems and kernels. Finally, we illustrate the agreement and disagreement between the MFM, SM and the underlying particle model for several numerical examples.
We consider walks on a triangular domain that is a subset of the triangular lattice. We then specialise this by dividing the lattice into two directed sublattices with different weights. Our central result is an explicit formula for the generating function of walks starting at a fixed point in this domain and ending anywhere within the domain. Intriguingly, the specialisation of this formula to walks starting in a fixed corner of the triangle shows that these are equinumerous to two-coloured Motzkin paths, and two-coloured three-candidate Ballot paths, in a strip of finite height.