ShantanuT01/DACTYL-Pretraining huggingface dataset:
We unify and generalize formulas obtained by Campillo, Delgado and Gusein-Zade in their series of articles. Positive results are established for rational and minimally elliptic singularities. By examples and counterexamples we also try to find the `limits' of these identities. Connections with the Seiberg-Witten Invariant Conjecture and Semigroup Density Conjecture are discussed.
We present the results of Monte Carlo simulations of a model of a single maghemite ferrimagnetic nanoparticle including radial surface anisotropy distinct from that in the core with the aim to clarify what is its role on the magnetization processes at low temperatures. The low temperature equilibrium states are analized and compared to those of a ferromagnetic particle with the same lattice structure. We have found that the formation of hedgehog-like structures due to increased surface anisotropy is responsible for a change in the reversal mechanism of the particles.
The recent variability survey of the NGC 3766 cluster revealed a considerable number of periodic variable stars in a region of the H-R diagram where no pulsation is expected. This region lies between the instability strips of the delta Scuti and SPB stars. Moreover the periods of the new phenomenon, P~0.1-0.7 d, do not allow to associate it a priori to either of these two types of pulsations. Stars in the NGC 3766 cluster are known as fast rotators with rotational velocities typically larger than half of their critical velocity. Rotation can affect both the geometrical properties and period domain of pulsations. It also alters the apparent stellar luminosity through gravity darkening, effect seldom taken considered in theoretical studies of the rotation-pulsation interaction. We explore if both of these effects are able to deliver a consistent interpretation for the observed properties of the "new variables" in NGC 3766: explaining their presence outside the known instability strips and their variability periods. We carry out an instability analysis of SPB models within the framework of the Traditional Approximation of Rotation and study the visibility of modes according to the angle of view and rotation. We also check how gravity darkening affects the effective temperature and luminosity of stellar models for different angles of view and rotation velocities. At the red (cold) border of the instability strip, prograde sectoral modes are preferentially excited and their visibilities are maximum when seen equator-on. Furthermore low-mass SPB models seen equator-on can appear in the gap between non-rotating SPB and delta Scuti stars due to gravity darkening. In that case, periods of these most visible modes are shifted to the 0.2-0.5 d range due to the effects of the Coriolis force. We hence suggest that the new variable stars observed in NGC 3766 are actually fast rotating SPB pulsators.
The status of the macroscopic and microscopic description of the collective quadrupole modes is reviewed, where limits due to non-adiabaticity and decoherence are exposed. The microscopic description of the yrast states in vibrator-like nuclei in the framework of the rotating mean field is presented.
A surface-acoustic-wave (SAW) driven light-emitting-diode structure that can implement a single-photon-source for quantum-cryptography applications is demonstrated. Our lateral n-i-p junction is realized starting from an undoped GaAs/AlGaAs quantum well by gating. It incorporates interdigitated transducers for SAW generation and lateral gates for current control. We demonstrate acoustoelectric transport and SAW-driven electroluminescence. The acoustoelectric current can be controlled down to complete pinch-off by means of the lateral gates.
Ruthenium compounds play prominent roles in materials research ranging from oxide electronics to catalysis, and serve as a platform for fundamental concepts such as spin-triplet superconductivity, Kitaev spin-liquids, and solid-state analogues of the Higgs mode in particle physics. However, basic questions about the electronic structure of ruthenates remain unanswered, because several key parameters (including the Hund's-rule, spin-orbit, and exchange interactions) are comparable in magnitude, and their interplay is poorly understood - partly due to difficulties in synthesizing sizable single crystals for spectroscopic experiments. Here we introduce a resonant inelastic x-ray scattering (RIXS) technique capable of probing collective modes in microcrystals of $4d$-electron materials. We present a comprehensive set of data on spin waves and spin-state transitions in the honeycomb antiferromagnet SrRu$_{2}$O$_{6}$, which possesses an unusually high N\'eel temperature. The new RIXS method provides fresh insight into the unconventional magnetism of SrRu$_{2}$O$_{6}$, and enables momentum-resolved spectroscopy of a large class of $4d$ transition-metal compounds.
Self-organization properties of sustained magnetized plasma are applied to selected solar data to understand solar magnetic fields. Torsional oscillations are speed-up and slow-down bands of the azimuthal flow that correlate with the solar cycle, and they imply the existence of a symmetric solar dynamo with a measured polar flux of 3x10^14 Wb. It is shown that the solar dynamo is thin (~0.1 Mm gradient scale size) and powerful (~10^23 W). These properties are found from the amplitude of the torsional oscillations and the relationship of their velocity contours to solar magnetograms supports the result. The dynamo has enough power to heat the chromosphere and to power the corona and the solar wind. The dynamo also causes a rigid rotation of the heliosphere out to at least the corona and the relationship of the rotation of the corona to solar magnetograms supports this result as well. The thin solar dynamo sustains a thin stable minimum energy state that seems to be covering most of the solar surface just below the photosphere. The magnetic field lines of the minimum energy state should be parallel to the solar surface and rotate with distance from the surface with 2{\pi} radians of rotation in ~1 Mm Resistive diffusion helps to push the magnetic fields to the surface and the global magnetic structure (GMS) seems to lose {\pi} radians every 11 years, causing the observed 180 degree flipping of the solar magnetic field. The thin sheets of magnetized plasma in solar prominences may be the lost thin sheets of the GMS. For completeness, the formation of sunspots, CMEs and flares is discussed.
Using a lattice equation of state combined with the D-dimensional Tolman-Oppenheimer-Volkoff equation and the Friedmann equations, we investigate the possibility of the formation of compact objects as well as the time evolution of the scale factor and the density profile of a self-gravitating material cluster. The numerical results show that in a $2+1$ dimensional spacetime, the mass is independent of the central pressure. Hence, the formation of only compact objects with a finite constant mass similar to the white dwarf is possible. However, in a $3+1$ dimensional spacetime, self-gravity leads to the formation of compact objects with a large gap of mass and the corresponding phase diagram has the same structure as the one for Neutron Star. The results also show that beyond certain critical central pressure, the star is unstable against gravitational collapse, and it may end in a black hole. Analysis of spacetimes of higher dimensions shows that gravity has the stronger effect in $3+1$ dimensions. Numerical solutions of the Friedmann equations show that the effect of the curvature of spacetime increases with increasing temperature, but decreases with increasing dimensionality beyond $D=3$.
We explore the magnetically-ordered ground state of the isovalently-substituted Mott-insulator Y$_{1-x}$La$_{x}$TiO$_{3}$ for $x$ $\leq$ 0.3 via single crystal growth, magnetometry, neutron diffraction, x-ray magnetic circular dichroism (XMCD), muon spin rotation ($\mu$SR) and small-angle neutron scattering (SANS). We find that the decrease in the magnetic transition temperature on approaching the ferromagnetic (FM) - antiferromagnetic (AFM) phase boundary at the La concentration $x_c$ $\approx$ 0.3 is accompanied by a strong suppression of both bulk and local ordered magnetic moments, along with a volume-wise separation into magnetically-ordered and paramagnetic regions. The thermal phase transition does not show conventional second-order behavior, since neither a clear signature of dynamic critical behavior nor a power-law divergence of the magnetic correlation length is found for the studied substitution range; this finding becomes increasingly obvious with substitution. Finally, from SANS and magnetometry measurements, we discern a crossover from easy-axis to easy-plane magneto-crystalline anisotropy with increasing La substitution. These results indicate complex changes in magnetic structure upon approaching the phase boundary.
N-body simulations of galactic collisions are employed to investigate the formation of elliptical rings in disk galaxies. The relative inclination between disk and dwarf galaxies is studied with a fine step of five degrees. It is confirmed that the eccentricity of elliptical ring is linearly proportional to the inclination angle. Deriving from the simulational results, an analytic formula which expresses the eccentricity as a function of time and inclination angle is obtained. This formula shall be useful for the interpretations of the observations of ring systems, and therefore reveals the merging histories of galaxies.
We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all regular sequences. Our results shed new light on the foundation of spectral analysis and on the asymptotic distribution of periodogram, and it provides a nice blend of harmonic analysis, theory of stationary processes and theory of martingales.
We introduce a new procedure to construct weight factors, which flatten the probability density of the overlap with respect to some pre-defined reference configuration. This allows one to overcome free energy barriers in the overlap variable. Subsequently, we generalize the approach to deal with the overlaps with respect to two reference configurations so that transitions between them are induced. We illustrate our approach by simulations of the brainpeptide Met-enkephalin with the ECEPP/2 energy function using the global-energy-minimum and the second lowest-energy states as reference configurations. The free energy is obtained as functions of the dihedral and the root-mean-square distances from these two configurations. The latter allows one to identify the transition state and to estimate its associated free energy barrier.
The significance of the magnitude of Prandtl number of a fluid in the propagation direction of induced convection rolls is elucidated. Specifically, we report on the physical mechanism to account for the formation and orientation of previously unexplored supra-wavelength periodic surface structures in dielectrics, following melting and subsequent capillary effects induced upon irradiation with ultrashort laser pulses. Counterintuitively, it is found that such structures exhibit periodicities, which are markedly, even multiple times, higher than the laser excitation wavelength. It turns out that the extent to which the hydrothermal waves relax depends upon the laser beam energy, produced electron densities upon excitation with femtosecond pulsed lasers, magnitude of the induced initial local roll disturbances and the magnitude of the Prandtl number with direct consequences on the orientation and size of the induced structures. It is envisaged that this elucidation may be useful for the interpretation of similar, albeit large-scale periodic or quasi-periodic structures formed in other natural systems due to thermal gradients, while it can also be of great importance for potential applications in biomimetics.
We observed an H$\alpha$ surge occurred in the active region NOAA 12401 on 2015 August 17, and discuss its trigger mechanism, kinematic and thermal properties. It is suggested that this surge is caused by a chromospheric reconnection which ejects cool and dense material with the transverse velocity about 21-28 km s$^{-1}$ and the initial doppler velocity of 12 km s$^{-1}$. This surge is similar to the injection of newly formed filament materials from their footpoints, except that the surge here occurred in a relatively weak magnetic environment of ~100 G. Thus we discuss the possibility of filament material replenishment via the erupting mass in such a weak magnetic field, which is often associated with quiescent filaments. It is found that the local plasma can be heated up to about 1.3 times of original temperature, which results in an acceleration about -0.017 km s$^{-2}$. It can lift the dense material up to 10 Mm and higher with a inclination angle smaller than 50$^{\circ}$, namely typical height of active region filaments. But it can hardly inject the material up to those filaments higher than 25 Mm, namely some quiescent filaments. Thus we think injection model does not work well in the formation of quiescent filaments.
The Bose-Hubbard model in an external magnetic field is investigated with strong-coupling perturbation theory. The lowest-order secular equation leads to the problem of a charged particle moving on a lattice in the presence of a magnetic field, which was first treated by Hofstadter. We present phase diagrams for the two-dimensional square and triangular lattices, showing a change in shape of the phase lobes away from the well-known power-law behavior in zero magnetic field. Some qualitative agreement with experimental work on Josephson-junction arrays is found for the insulating phase behavior at small fields.
BL Lac objects are known to have very energetic jets pointing towards the observer under small viewing angles. Many of these show high luminosity over the whole energy range up to TeV, mostly classified as high-energy peaked BL Lac objects. Recently, TeV gamma-ray emission was detected from a low-energy peaked BL Lac object. Interestingly, this source has also a clear detection of an X-ray jet. We present a detailed study of this X-ray jet and its connection to the radio jet as well as a study of the underlying physical processes in the energetic jet, producing emission from the radio to the TeV range.
We demonstrate the feasibility of a strong feedback regime for a single-electron tunneling device weakly coupled to an underdamped single-mode oscillator. In this regime, mechanical oscillations are generated and the current is strongly modified whereas the current noise is parametrically big with respect to the Poisson value. This regime requires energy dependence of the tunnel amplitudes. For sufficiently fast tunnel rates the mechanical contribution to current noise can exceed the Poisson value even beyond the strong feedback regime.
By borrowing the wisdom of human in gaze following, we propose a two-stage solution for gaze point prediction of the target persons in a scene. Specifically, in the first stage, both head image and its position are fed into a gaze direction pathway to predict the gaze direction, and then multi-scale gaze direction fields are generated to characterize the distribution of gaze points without considering the scene contents. In the second stage, the multi-scale gaze direction fields are concatenated with the image contents and fed into a heatmap pathway for heatmap regression. There are two merits for our two-stage solution based gaze following: i) our solution mimics the behavior of human in gaze following, therefore it is more psychological plausible; ii) besides using heatmap to supervise the output of our network, we can also leverage gaze direction to facilitate the training of gaze direction pathway, therefore our network can be more robustly trained. Considering that existing gaze following dataset is annotated by the third-view persons, we build a video gaze following dataset, where the ground truth is annotated by the observers in the videos. Therefore it is more reliable. The evaluation with such a dataset reflects the capacity of different methods in real scenarios better. Extensive experiments on both datasets show that our method significantly outperforms existing methods, which validates the effectiveness of our solution for gaze following. Our dataset and codes are released in https://github.com/svip-lab/GazeFollowing.
Two dimensional electron gases based on SrTiO$_3$ are an intriguing platform for exploring mesoscopic superconductivity combined with spin-orbit coupling, offering electrostatic tunability from insulator to metal to superconductor within a single material. So far, however, quantum effects in SrTiO$_3$ nanostructures have been complicated by disorder. Here we introduce a facile approach to achieving high mobility and patterning gate-tunable structures in SrTiO$_3$, and use it to demonstrate ballistic constrictions with clean normal state conductance quantization. Conductance plateaus show two-fold degeneracy that persists to magnetic fields of at least 5 T - far beyond what one would expect from the $g$-factor extracted at high fields - a potential signature of electron pairing extending outside the superconducting regime.
We report an analysis of the dynamical structure of clusters of galaxies from a survey of photometric and spectroscopic observations in the fields of southern Abell Clusters. We analyze the galaxy velocity field in extended regions up to 7 h^-1 Mpc from cluster centers and we estimate mean velocity dispersions and their radial dependence. Only one from a total number of 41 Abell clusters does not correspond to a dynamically bound system. However, four of these bound objects are double clusters. We estimate that 20 % (7 clusters) of the 35 remaining are subject to serious projection effects. Normalizing the clustercentric distances by means of the overdensity radius r_200, and the velocity dispersion profiles (VDPs) by the corresponding mean cluster velocity dispersion, we computed the average VDP. Our results indicate a flat behavior of the mean VDP at large distances from the cluster center. Nevertheless, we found that for the inner part of the clusters (r/r_200 leq 1) the VDP is up to a 10% smaller than at larger radii.
Quantum discord is an important measure of quantum correlations that can serve as a resource for certain types of quantum information processing. \ Like entanglement, discord is subject to destruction by external noise. The routes by which this destruction can take place depends on the shape of the hypersurface of zero discord $\mathcal{C}$ in the space of generalized Bloch vectors. For 2 qubits, we show that with a few points subtracted, this hypersurface is a simply-connected 9-dimensional manifold embedded in a 15-dimensional background space. \ We do this by constructing an explicit\ homeomorphism from a known manifold to the subtracted version of $\mathcal{C} $. We also construct a coordinate map on $\mathcal{C}$ that can be used for integration or other purposes. This topological characterization of $% \mathcal{C}$ has important implications for the classification of the possible time evolutions of discord in physical models. The classification for discord contrasts sharply with the possible evolutions of entanglement.   Using topological methods, we classify the possible joint evolutions of entanglement and discord. There are 9 allowed categories: 6 categories for a Markovian process and 3 categories for a non-Markovian process, respectively. We illustrate these conclusions with an anisotropic XY spin model. All 9 categories can be obtained by adjusting parameters.
The longitudinal response function of 4He is calculated with the Argonne V18 potential. The comparison with experiment suggests the need of a three-body force. When adding the Urbana IX three-body potential in the calculation of the lower longitudinal multipoles, the total strength is suppressed in the quasi-elastic peak, towards the trend of the experimental data.
To pinpoint the peak location of the synchrotron total intensity emission in a spiral arm, we use a map of the spiralarm locations (from the observed arm tangent). Thus In a typical spiral arm in Galactic Quadrant I, we find the peak of the synchrotron radiation to be located about 220 +/-40 pc away from the inner arm edge (hot dust lane) inside the spiral arm. While most of the galactic disk has a clockwise largescale magnetic field, we make a statistical analysis to delimitate more precisely the smaller reverse annulus wiith a counterclockwise galactic magnetic field. We find an annulus width of 2.1 +/-0.3 kpc (measured along the Galactic radius), located from 5.5 to 7.6 kpc from the Galactic Center). The annulus does not overlay with a single spiral arm -- it encompasses segments of two different spiral arms. Using a recent delineation of the position of spiral arms, the field-reversed annulus is seen to encompass the Crux-Centaurus arm (in Galactic Quadrant IV) and the Sagittarius arm (in Galactic Quadrant I).
Counting functions are constructed for sums of integers raised to a fixed positive rational power. That is, given values formed by $u_1^{j/k} + u_2^{j/k} + ... + u_l^{j/k}$, $u_i \in \mathbb{Z}^+$, the number of values less than or equal to a given $w>0$ is determined. The counting functions developed are framed in terms of convolution exponentials, and are closely related to the Riemann zeta function. At the conclusion, several estimates are derived, with special emphasis on the case of sums of square roots, i.e. $j=1$, $k=2$.
Numerous spectroscopic observations provide compelling evidence for a non-canonical mixing process that modifies the surface abundances of Li, C and N of low-mass red giants when they reach the bump in the luminosity function. Eggleton et al. (2006) have proposed that a molecular weight inversion created by the 3He(3He,2p)4He reaction may be at the origin of this mixing, and relate it to the Rayleigh-Taylor instability. In the present work we argue that one is actually dealing with a double diffusive instability referred to as thermohaline convection and we discuss its influence on the red giant branch. We compute stellar models of various initial metallicities using the prescription by Ulrich (1972) (extended to the case of a non-perfect gas) for the turbulent diffusivity produced by the thermohaline instability in stellar radiation zones. Thermohaline mixing simultaneously accounts for the observed behaviour of the carbon isotopic ratio and of the abundances of Li, C and N on the upper part of the red giant branch. It reduces significantly the 3He production with respect to canonical evolution models as required by measurements of 3He/H in galactic HII regions. Thermohaline mixing is a fundamental physical process that must be included in stellar evolution modeling.
Let $L$ be a finite sequence of natural numbers. In Woryna (2017,2018), we derived some interesting properties for the ratio $\rho_{n,L}=|PR_n(L)|/|UD_n(L)|$, where $UD_n(L)$ denotes the set of all codes over an $n$-letter alphabet and with length distribution $L$, and $PR_n(L)\subseteq UD_n(L)$ is the corresponding subset of prefix codes. In the present paper, we study the case when the length distributions are three-element sequences. We show in this case that the ratio $\rho_{n,L}$ is always greater than $\alpha_n$, where $\alpha_n=(n-2)/n$ for $n>2$ and $\alpha_2=1/6$. Moreover, the number $\alpha_n$ is the best possible lower bound for this ratio, as the length distributions of the form $L=(1,1,c)$ and $L=(1,2,c)$ assure that the ratios asymptotically approach $\alpha_n$. Namely, if $L=(1,1,c)$, then $\rho_{n,L}$ tends to $(n-2)/n$ with $c\to\infty$, and, if $L=(1,2,c)$, then $\rho_{2,L}$ tends to $1/6$ with $c\to\infty$.