ShantanuT01/DACTYL-Pretraining huggingface dataset:
Non-adiabatic effects play an important role in many chemical processes. In order to study the underlying non-adiabatic potential-energy surfaces (PESs), we present a locally-constrained density-functional theory approach, which enables us to confine electrons to sub-spaces of the Hilbert space, e.g. to selected atoms or groups of atoms. This allows to calculate non-adiabatic PESs for defined charge and spin states of the chosen subsystems. The capability of the method is demonstrated by calculating non-adiabatic PESs for the scattering of a sodium and a chlorine atom, for the interaction of a chlorine molecule with a small metal cluster, and for the dissociation of an oxygen molecule at the Al(111) surface.
Given a number field $L$, we define the degree of an algebraic number $v \in L$ with respect to a choice of a primitive element of $L$. We propose the question of computing the minimal degrees of algebraic numbers in $L$, and examine these values in degree $4$ Galois extensions over $\mathbb{Q}$ and triquadratic number fields. We show that computing minimal degrees of non-rational elements in triquadratic number fields is closely related to solving classical Diophantine problems such as congruent number problem as well as understanding various arithmetic properties of elliptic curves.
We present a detailed photometric study and measurements of spiral arm pitch angles for a sample of 50 non-barred or weakly barred grand-design spiral galaxies selected from Sloan Digital Sky Survey. In order to find pitch angles, we used a new method based on the window Fourier analysis of their images. This method allows us not only to infer the average pitch angle, but to obtain its value as a function of galactocentric radius as well. Our main results are as follows:   (1) Spiral arms of most galaxies cannot be described by a single value of the pitch angle. About 2/3 of galaxies demonstrate pitch angle variations exceeding 20%. In most galaxies in the sample their pitch angle decreases by increasing the distance from the centre.   (2) Pitch angle variations correlate with the properties of galaxies - with the shape of the surface brightness distribution (envelope-type or truncated disc), and with the sign of stellar disc colour gradient.   (3) More luminous and bright bulges produce more tightly wound spiral arms, that is in agreement with current models for spiral arms formation.
In this paper, we investigate the existence of solution for systems of Fokker-Planck equations coupled through a common nonlinear congestion. Two different kinds of congestion are considered: a porous media congestion or \textit{soft} congestion and the \textit{hard} congestion given by the constraint $\rho_1+\rho_2 \leqslant 1$. We show that these systems can be seen as gradient flows in a Wasserstein product space and then we obtain a constructive method to prove the existence of solutions. Therefore it is natural to apply it for numerical purposes and some numerical simulations are included.
Let $\xi_1,\xi_2,\ldots$ be independent, identically distributed random variables with infinite mean $\mathbf E[|\xi_1|]=\infty.$ Consider a random walk $S_n=\xi_1+\cdots+\xi_n$, a stopping time $\tau=\min\{n\ge 1: S_n\le 0\}$ and let $M_\tau=\max_{0\le i\le \tau} S_i$. We study the asymptotics for $\mathbf P(M_\tau>x),$ as $x\to\infty$.
Aims. The optical emission of black hole transients increases by several magnitudes during the X-ray outbursts. Whether the extra light arises from the X-ray heated outer disc, from the inner hot accretion flow, or from the jet is currently debated. Optical polarisation measurements are able to distinguish the relative contributions of these components. Methods. We present the results of BVR polarisation measurements of the black hole X-ray binary MAXI J1820+070 during the period of March-April 2018. Results. We detect small, $\sim$0.7%, but statistically significant polarisation, part of which is of interstellar origin. Depending on the interstellar polarisation estimate, the intrinsic polarisation degree of the source is between $\sim$0.3% and 0.7%, and the polarisation position angle is between $\sim10\deg-30\deg$. We show that the polarisation increases after MJD 58222 (2018 April 14). The change is of the order of 0.1% and is most pronounced in the R band. The change of the source Stokes parameters occurs simultaneously with the drop of the observed V-band flux and a slow softening of the X-ray spectrum. The Stokes vectors of intrinsic polarisation before and after the drop are parallel, at least in the V and R filters. Conclusions. We suggest that the increased polarisation is due to the decreasing contribution of the non-polarized component, which we associate with the the hot flow or jet emission. The low polarisation can result from the tangled geometry of the magnetic field or from the Faraday rotation in the dense, ionised, and magnetised medium close to the black hole. The polarized optical emission is likely produced by the irradiated disc or by scattering of its radiation in the optically thin outflow.
We study the in-medium properties of mesons $(\pi,\eta,\rho)$ and baryon resonances in cold nuclear matter within a coupled-channel analysis. The meson self energies are generated by particle-hole excitations. Thus multi-peak spectra are obtained for the mesonic spectral functions. In turn this leads to medium-modifications of the baryon resonances. Special care is taken to respect the analyticity of the spectral functions and to take into account effects from short-range correlations both for positive and negative parity states. Our model produces sensible results for pion and $\Delta$ dynamics in nuclear matter. We find a strong interplay of the $\rho$ meson and the $D_{13}(1520)$, which moves spectral strength of the $\rho$ spectrum to smaller invariant masses and leads to a broadening of the baryon resonance. The optical potential for the $\eta$ meson resulting from our model is rather attractive whereas the in-medium properties modifications of the $S_{11}(1535)$ are found to be quite small.
Modelling the morphology of a nova outburst provides valuable information on the shaping mechanism in operation at early stages following the outburst. We performed morpho-kinematical studies, using {\sc shape}, of the evolution of the H\alpha\ line profile following the outburst of the nova KT Eridani. We applied a series of geometries in order to determine the morphology of the system. The best fit morphology was that of a dumbbell structure with a ratio between the major to minor axis of 4:1, with an inclination angle of 58$^{+6}_{-7}$ degrees and a maximum expansion velocity of 2800$\pm$200 km/s. Although, we found that it is possible to define the overall structure of the system, the radial density profile of the ejecta is much more difficult to disentangle. Furthermore, morphology implied here may also be consistent with the presence of an evolved secondary as suggested by various authors.
From the analysis of more than 92 ks of data obtained with the laxpc instrument on board Astrosat we have detected a clear high-frequency QPO whose frequency varies between 67.4 and 72.3 Hz. In the classification of variability classes of GRS 1915+105, at the start of the observation period the source was in class omega and at the end the variability was that of class mu: both classes are characterized by the absence of hard intervals and correspond to disk-dominated spectra. After normalization to take into account time variations of the spectral properties as measured by X-ray hardness, the QPO centroid frequency is observed to vary along the hardness-intensity diagram, increasing with hardness. We also measure phase lags that indicate that HFQPO variability at high energies lags that at lower energies and detect systematic variations with the position on the hardness-intensity diagram. This is the first time that (small) variations of the HFQPO frequency and lags are observed to correlate with other properties of the source. We discuss the results in the framework of existing models, although the small (7%) variability observed is too small to draw firm conclusions.
This preprint mainly reflects the new chapter we are prepearing for the second edition of our book "Gravitational Solitons" (V. Belinski and E. Verdaguer). However, here it is written in the form of more or less self-consistent paper dedicated to the mathematical theory of black holes immersed in the external electromagnetic field. The purpose of this development is to describe the procedure by which one can construct a number of axially symmetric black holes or naked singularities arranged along the symmetry axis and immersed in an (also axially symmetric) external electromagnetic field.
Magnetism at the nanoscale has been a very active research area in the past decades, because of its novel fundamental physics and exciting potential applications. We have recently performed an {\it ab intio} study of the structural, electronic and magnetic properties of all 3$d$ transition metal (TM) freestanding atomic chains and found that Fe and Ni nanowires have a giant magnetic anisotropy energy (MAE), indicating that these nanowires would have applications in high density magnetic data storages. In this paper, we perform density functional calculations for the Fe, Co and Ni linear atomic chains on Cu(001) surface within the generalized gradient approximation, in order to investigate how the substrates would affect the magnetic properties of the nanowires. We find that Fe, Co and Ni linear chains on Cu(001) surface still have a stable or metastable ferromagnetic state. When spin-orbit coupling (SOC) is included, the spin magnetic moments remain almost unchanged, due to the weakness of SOC in 3$d$ TM chains, whilst significant orbital magnetic moments appear and also are direction-dependent. Finally, we find that the MAE for Fe, and Co remains large, i.e., being not much affected by the presence of Cu substrate.
We consider a two-phase heat conductor in $\mathbb R^N$ with $N \geq 2$ consisting of a core and a shell with different constant conductivities. Suppose that, initially, the conductor has temperature 0 and, at all times, its boundary is kept at temperature 1.   It is shown that, if there is a stationary isothermic surface in the shell near the boundary, then the structure of the conductor must be spherical. Also, when the medium outside the two-phase conductor has a possibly different conductivity, we consider the Cauchy problem with $N \ge 3$ and the initial condition where the conductor has temperature 0 and the outside medium has temperature 1. Then we show that almost the same proposition holds true.
Let $\mathcal{G}(k)$ denote the set of connected $k$-regular graphs $G$, $k\geq2$, where the number of vertices at distance 2 from any vertex in $G$ does not exceed $k$. Asratian (2006) showed (using other terminology) that a graph $G\in\mathcal{G}(k)$ is Hamiltonian if for each vertex $u$ of $G$ the subgraph induced by the set of vertices at distance at most 2 from $u$ is 2-connected. We prove here that in fact all graphs in the sets $\mathcal{G}(3)$, $\mathcal{G}(4)$ and $\mathcal{G}(5)$ are Hamiltonian. We also prove that the problem of determining whether there exists a Hamilton cycle in a graph from $\mathcal{G}(6)$ is NP-complete. Nevertheless we show that every locally connected graph $G\in\mathcal{G}(k)$, $k\geq6$, is Hamiltonian and that for each non-Hamiltonian cycle $C$ in $G$ there exists a cycle $C'$ of length $|V(C)|+\ell$ in $G$, $\ell\in\{1,2\}$, such that $V(C)\subset V(C')$. Finally, we note that all our conditions for Hamiltonicity apply to infinitely many graphs with large diameters.
In order to analyze some low energy experimental anomalies, we charge with a non-universal $U(1)'$ gauge symmetry the standard model fermions, taking as a starting point the well-known scotogenic model. In order to have non-trivial solutions to the anomalies and the Yukawa constraints, we add three neutral singlet Dirac fermions. We have found two possible non-universal solutions which, as a matter of principle, are suitable to analyze family-dependent experimental anomalies.
We have measured the abundances of Fe, Si, Ni, Ti, and Na in 20 Pleiads with \teff values near solar and with low \vsini using high-resolution, high signal-to-noise echelle spectra. We have validated our procedures by also analyzing 10 field stars of a range of temperatures and metallicities that were observed by \citet{Vale05}. Our result for the Pleiades is [Fe/H] = $+0.03\pm0.02\pm0.05$ (statistical and systematic). The average of published measurements for the Pleiades is $+0.042\pm0.021$.
The Relativistic Distorted-Wave Impulse Approximation is used to describe the $^3$He($e,e^\prime p$)$^2$H process. We describe the $^3$He nucleus within the adiabatic hyperspherical expansion method with realistic nucleon-nucleon interactions. The overlap between the $^3$He and the deuteron wave functions can be accurately computed from a three-body calculation. The nucleons are described by solutions of the Dirac equation with scalar and vector (S-V) potentials. The wave function of the outgoing proton is obtained by solving the Dirac equation with a S-V optical potential fitted to elastic proton scattering data on the residual nucleus. Within this theoretical framework, we compute the cross section of the reaction and other observables like the transverse-longitudinal asymmetry, and compare them with the available experimental data measured at JLab.
In this paper the hybrid-NLIE approach of [38] is extended to the ground state of a D-brane anti-D-brane system in AdS/CFT. The hybrid-NLIE equations presented in the paper are finite component alternatives of the previously proposed TBA equations and they admit an appropriate framework for the numerical investigation of the ground state of the problem. Straightforward numerical iterative methods fail to converge, thus new numerical methods are worked out to solve the equations. Our numerical data confirm the previous TBA data. In view of the numerical results the mysterious L = 1 case is also commented in the paper.
Heavy nuclei bombarded with protons and deuterons in the 1 GeV range have a large probability of undergoing a process of evaporation and fission; less frequently, the prompt emission of few intermediate-mass fragments can also be observed.   We employ a recently developed microscopic approach, based on the Boltzmann-Langevin transport equation, to investigate the role of mean-field dynamics and phase-space fluctuations in these reactions.   We find that the formation of few IMF's can be confused with asymmetric fission when relying on yield observables, but it can not be assimilated to the statistical decay of a compound nucleus when analysing the dynamics and kinematic observables: it can be described as a fragmentation process initiated by phase-space fluctuations, and successively frustrated by the mean-field resilience. As an extreme situation, which corresponds to non-negligible probability, the number of fragments in the exit channel reduces to two, so that fission-like events are obtained by re-aggregation processes.   This interpretation, inspired by nuclear-spallation experiments, can be generalised to heavy-ion collisions from Fermi to relativistic energies, for situations when the system is closely approaching the fragmentation threshold.
Considerable efforts have been made in recent years to theoretically understand quantum phase transitions in Kondo lattice systems. A particular focus is on Kondo destruction, which leads to quantum criticality that goes beyond the Landau framework of order-parameter fluctuations. This unconventional quantum criticality has provided an understanding of the unusual dynamical scaling observed experimentally. It has also predicted a sudden jump of the Fermi surface and an extra (Kondo destruction) energy scale, both of which have been verified by systematic experiments. Considerations of Kondo destruction have in addition yielded a global phase diagram, which has motivated the current interest in heavy fermion materials with variable dimensionality or geometrical frustration. Here we summarize these developments, and discuss some of the ongoing work and open issues. We also consider the implications of these results for superconductivity. Finaly, we address the effect of spin-orbit coupling on the global phase diagram, suggest that SmB6 under pressure may display unconventional superconductivity in the transition regime between a Kondo insulator phase and an antiferroamgnetic metal phase, and argue that the interfaces of heavy-fermion heterostructures will provide a fertile setting to explore topological properties of both Kondo insulators and heavy-fermion superconductors.
It is demonstrated that the nearest neighbor Mn pair on the GaAs (001) surface has a lower energy for the [-110] direction comparing to the [110] case. According to the group theory and the Luttinger's method of invariants, this specific Mn distribution results in bulk uniaxial in-plane and out-of-plane anisotropies. The sign and magnitude of the corresponding anisotropy energies determined by a perturbation method and ab initio computations are consistent with experimental results.
We begin with a review of the predictions for cycle~24 before its onset. After summarizing the basics of the flux transport dynamo model, we discuss how this model had been used to make a successful prediction of cycle~24, on the assumption that the irregularities of the solar cycle arise due to the fluctuations in the Babcock--Leighton mechanism. We point out that fluctuations in the meridional circulation can be another cause of irregularities in the cycle.
Temporal offsets between the time series of solar activity indicators provide important clues regarding the physical processes responsible for the cyclic variability in the solar atmosphere. Hysteresis patterns generated between any two indicators were popularly used to study their morphological features and further to understand their inter relationships. We use time series of different solar indicators to understand the possible cause-and-effect criteria between their respective source regions. Sensitivity of the upper atmosphere to the activity underneath might play an important role in introducing different evolutionary patterns in the profiles of solar indicators and in turn cause temporal offsets between them. Limitations in the observations may also cause relative shifts in the time series.
The search for an alternative high-voltage polyanionic cathode material for Li-ion batteries is vital to improve the energy densities beyond the state-of-the-art, where sulfate frameworks form an important class of high-voltage cathode materials due to the strong inductive effect of the S$^{6+}$ ion. Here, we have investigated the mechanism of cationic and/or anionic redox in Li$_x$M(SO$_4$)$_2$ frameworks (M = Mn, Fe, Co, and Ni and 0 $\leq$ x $\leq$ 2) using density functional calculations. Specifically, we have used a combination of Hubbard $U$ corrected strongly constrained and appropriately normed (SCAN+$U$) and generalized gradient approximation (GGA+$U$) functionals to explore the thermodynamic (polymorph stability), electrochemical (intercalation voltage), geometric (bond lengths), and electronic (band gaps, magnetic moments, charge populations, etc.) properties of the bisulfate frameworks considered. Importantly, we find that the anionic (cationic) redox process is dominant throughout delithiation in the Ni (Mn) bisulfate, as verified using our calculated projected density of states, bond lengths, and on-site magnetic moments. On the other hand, in Fe and Co bisulfates, cationic redox dominates the initial delithiation (1 $\leq$ x $\leq$ 2), while anionic redox dominates subsequent delithiation (0 $\leq$ x $\leq$ 2). In addition, evaluation of the crystal overlap Hamilton population reveals insignificant bonding between oxidizing O atoms throughout the delithiation process in the Ni bisulfate, indicating robust battery performance that is resistant to irreversible oxygen evolution. Finally, we observe both GGA+$U$ and SCAN+$U$ predictions are in qualitative agreement for the various properties predicted. Our work should open new avenues for exploring lattice oxygen redox in novel high voltage polyanionic cathodes, especially using the SCAN+$U$ functional.
We study the most common image and informal description of the optimal transport problem for quadratic cost, also known as the second boundary value problem for the Monge--Amp\`{e}re equation -- What is the most efficient way to fill a hole with a given pile of sand? -- by proving regularity results for optimal transports between degenerate densities. In particular, our work contains an analysis of the setting in which holes and sandpiles are represented by absolutely continuous measures concentrated on bounded convex domains whose densities behave like nonnegative powers of the distance functions to the boundaries of these domains.
In this paper, we study combinatorial properties of quasi-Cartan companions defined by the c-vectors of acyclic skew-symmetrizable cluster algebras. In particular, we show that the diagram of any skew-symmetrizable matrix associated with an acyclic cluster algebra has an admissible cut of edges.
Looking in positive characteristic for failures of the Bertini-Sard theorem, we determine, up to birational equivalence, the separable proper morphisms of smooth algebraic varieties in characteristic two, whose fibres are non-smooth curves of arithmetic genus two.
Our goal is to determine the rotational and magnetic-related activity properties of stars at different stages of evolution. We have focussed our attention on 6 young loose stellar associations within 100 pc and ages in the range 8-70 Myr: TW Hydrae (~8 Myr), beta Pictoris (~10 Myr), Tucana/Horologium, Columba, Carina (~30 Myr), and AB Doradus (~70 Myr). Additional data on alpha Persei and the Pleiades from the literature is also considered. Rotational periods of stars showing rotational modulation due to photospheric magnetic activity (i.e. starspots) have been determined applying the Lomb-Scargle periodogram technique to photometric time-series obtained by the All Sky Automated Survey (ASAS). The magnetic activity level has been derived from the amplitude of the V lightcurves. We detected the rotational modulation and measured the rotation periods of 93 stars for the first time, and confirmed the periods of 41 stars already known from the literature. For further 10 stars we revised the period determinations by other authors. The sample was augmented with periods of 21 additional stars retrieved from the literature. In this way, for the first time we were able to determine largest set of rotation periods at ages of ~8, ~10 and ~30 Myr, as well as increase by 150\% the number of known periodic members of AB Dor.The analysis of the rotation periods in young stellar associations, supplemented by Orion Nebula Cluster (ONC) and NGC2264 data from the literature, has allowed us to find that in the 0.6 - 1.2 solar masses range the most significant variations of the rotation period distribution are the spin-up between 9 and 30 Myr and the spin-down between 70 and 110 Myr. Variations between 30 and 70 Myr are rather doubtful, despite the median period indicates a significant spin-up.