ShantanuT01/DACTYL-Pretraining huggingface dataset:
Two occupied native defect bands are detected in pure HfO2, with one located in the middle of the band gap and the other slightly above the valence band maximum. The investigation on the electronic structures of hafnium aluminate thin films as a function of Al concentration discloses the evolution of such bands while the density of states of the former one reduces drastically with the Al addition, that of the later one remains rather unaffected. Our first principles studies of the system attribute the two bands to the charged oxygen vacancy, and the oxygen interstitial related defect states of the HfO2, respectively. We further demonstrate that the observed evolution of the defect bands originates from the interaction in-between the added Al and the native defects of pure HfO2, which effectively passivates the VO+ induced mid-gap states but has little effect on other aspects of the electronic structure of the material.
We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler equations and the motion of the rigid bodies is given by Newton's laws with forces due to the fluid pressure. We prove that, for smooth solutions, Newton's equations can be recast as a second-order ODE for the degrees of freedom of the rigid bodies with coefficients depending on the fluid vorticity and on the circulations around the bodies, but not anymore on the fluid pressure. This reformulation highlights geodesic aspects linked to the added mass effect, gyroscopic features generalizing the Kutta-Joukowski-type lift force, including body-body interactions through the potential flows induced by the bodies' motions, body-body interactions through the irrotational flows induced by the bodies' circulations, and interactions between the bodies and the fluid vorticity.
We study the deformation theory of a Fano variety X with normal crossing singularities of dimension at most three. We obtain a formula for the sheaf T^1(X) of first order deformations of X in a suitable log resolution of X and its singular locus Z and we obtain explicit criteria for the existence of smoothings of X.
Many methods for computing electronic correlation effects at finite temperature are related to many-body perturbation theory in the grand-canonical ensemble. In most applications, however, the average number of electrons is known rather than the chemical potential, requiring that expensive correlation calculations must be repeated iteratively in search for the chemical potential that yields the desired average number of electrons. In extended systems with mobile charges, however, the long-ranged electrostatic interaction should guarantee that the average ratio of negative and positive charges is one for any finite chemical potential. All properties per electron are virtually independent of the chemical potential, as for instance in an electric wire at different voltage potentials.   This work shows that the infinite-size limit of the exchange-correlation free energy agrees with the infinite-size limit of the exchange-correlation grand potential at a non-interacting chemical potential. The latter requires only one expensive correlation calculation for each system size. Analogous to classical simulations of long-range-interacting particles, this work uses a regularization of the Coulomb interaction such that each electron on average interacts only with as many electrons as there are electrons in the simulation, avoiding interactions with periodic images.   Numerical calculations of the warm uniform electron gas have been conducted with the Spencer--Alavi regularization employing the finite-temperature Hartree approximation for the self-consistent field and linearized finite-temperature direct-ring coupled cluster doubles for treating correlation.
We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for all multipartite symmetric states in the general $N$-qubit case. For this purpose, we introduce 2 parameters playing a crucial role, namely the \emph{diversity degree} and the \emph{degeneracy configuration} of a symmetric state. Those parameters give rise to a simple method of identifying operational families of SLOCC entanglement classes of all symmetric $N$-qubit states, where the number of families grows as the partition function of the number of qubits.
We consider the final-state problem for the nonlinear Schr\"{o}dinger equations (NLS) with a suitable time-decaying harmonic oscillator. In this equation, the power of nonlinearity $|u|^{\rho}u $ is included in the long-range class if $0 < \rho \leq 2/(n(1- \lambda)) $ with $0 \leq \lambda <1/2$, which is determined by the harmonic potential and a coefficient of Laplacian. In this paper, we find the final state for this system and obtain the decay estimate for asymptotics.
We discuss the structure of auxiliary fields for non-Abelian BF theories in arbitrary dimensions. By modifying the classical BRST operator, we build the on-shell invariant complete quantum action. Therefore, we introduce the auxiliary fields which close the BRST algebra and lead to the invariant extension of the classical action.
We consider a class of parabolic stochastic PDEs on bounded domains $D\subseteq\mathbb{R}^d$ that includes the stochastic heat equation, but with a fractional power $\gamma$ of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces $H_r$, with $r < \gamma - d/2$, we study its power variations in $H_r$ along regular partitions of the time-axis. As the mesh size tends to zero, we find a phase transition at $r=-d/2$: the solutions have a nontrivial quadratic variation when $r<-d/2$ and a nontrivial $p$th order variation for $p= 2\gamma/(\gamma-d/2-r)>2$ when $r>-d/2$. More generally, suitably normalized power variations of any order satisfy a genuine law of large numbers in the first case and a degenerate limit theorem in the second case. When $r<-d/2$, the quadratic variation is given explicitly via an expression that involves the spectral zeta function, which reduces to the Riemann zeta function when $d=1$ and $D$ is an interval.
Since the end of the eighties and in response to a reported increase in the total neutrino flux in the Homestake experiment in coincidence with solar flares, solar neutrino detectors have searched for solar flare signals. Even though these detectors have used different solar flare samples and analyses, none of them has been able to confirm the possible signal seen by Homestake. Neutrinos from the decay of mesons, which are themselves produced in collisions of accelerated ions with the solar atmosphere would provide a novel window on the underlying physics of the hadronic acceleration and interaction processes during solar flares. Solar flare neutrino flux measurements would indeed help to constrain current parameters such as the composition of the accelerated flux, the proton/ion spectral index and the high energy cutoff or the magnetic configuration in the interaction region. We describe here a new way to search for these neutrinos by considering a specific solar flare sample and a data driven time window template which will improve the likelihood of neutrino detection.
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry, including gravitational collapse, critical phenomena, investigations of cosmic censorship, and head-on black hole collisions. Our objective here is to detail the (2+1)+1 formalism we use to arrive at the corresponding system of equations and the numerical methods we use to solve them. We are able to obtain stable evolution, despite the singular nature of the coordinate system on the axis, by enforcing appropriate regularity conditions on all variables and by adding numerical dissipation to hyperbolic equations.
Very recent measurements of stellar winds are used to update relations between winds and coronal activity. New wind constraints include an upper limit of Mdot<0.1 Mdot_sun for Tau Ceti (G8 V), derived from a nondetection of astrospheric H I Lyman-alpha absorption. This upper limit is reported here for the first time, and represents the weakest wind constrained using the astrospheric absorption technique. A high mass loss rate measurement of Mdot=10 Mdot_sun for Delta Pav (G8 IV) from astrospheric Lyman-alpha absorption suggests stronger winds for subgiants than for main sequence stars of equivalent activity. A very low mass-loss rate of Mdot~0.06 Mdot_sun recently estimated for GJ 436 (M3 V) from Lyman-alpha absorption from an evaporating exoplanetary atmosphere implies inactive M dwarfs may have weak winds compared with GK dwarfs of similar activity.
A complete set for pseudoscalar-meson photoproduction is a minimum set of observables from which one can determine the underlying reaction amplitudes unambiguously. The complete sets considered in this work involve single- and double-polarization observables. It is argued that for extracting amplitudes from data, the transversity representation of the reaction amplitudes offers advantages over alternate representations. It is shown that with the available single-polarization data for the p({\gamma},K^+)\Lambda reaction, the energy and angular dependence of the moduli of the normalized transversity amplitudes in the resonance region can be determined to a fair accuracy. Determining the relative phases of the amplitudes from double-polarization observables is far less evident.
Space-based gravitational-wave (GW) detectors, including LISA, Taiji and TianQin, are able to detect mHz GW signals produced by mergers of supermassive black hole binaries, which opens a new window for GW astronomy. In this article, we numerically estimate the potential capabilities of the future networks of multiple space-based detectors using Bayesian analysis. We modify the public package Bilby and employ the sampler PyMultiNest to analyze the simulated data of the space-based detector networks, and investigate their abilities for source localization and testing the parity symmetry of gravity. In comparison with the case of an individual detector, we find detector networks can significantly improve the source localization. While for constraining the parity symmetry of gravity, we find that detector networks and an individual detector follow the similar constraints on the parity-violating energy scale $M_{\rm PV}$. Similar analysis can be applied to other potential observations of various space-based GW detectors.
We use the IllustrisTNG simulations to explore the dynamic scaling relation between massive clusters and their central galaxies (BCGs). The Illustris TNG300-1 simulation we use includes 280 massive clusters with $M_{200} > 10^{14}$ M$_{\odot}$ enabling a robust statistical analysis. We derive the line-of-sight velocity dispersion of the stellar particles of the BCGs ($\sigma_{*, BCG}$), analogous to the observed BCG stellar velocity dispersion. We also compute the subhalo velocity dispersion to measure the cluster velocity dispersion ($\sigma_{cl}$). Both $\sigma_{*, BCG}$ and $\sigma_{cl}$ are proportional to the cluster halo mass, but the slopes differ slightly. Thus like the observed relation, $\sigma_{*, BCG} / \sigma_{cl}$ declines as a function of $\sigma_{cl}$, but the scatter is large. We explore the redshift evolution of $\sigma_{*, BCG} - \sigma_{cl}$ scaling relation for $z \lesssim 1$ in a way that can be compared directly with observations. The scaling relation has a similar slope at high redshift, but the scatter increases because of the large scatter in $\sigma_{*, BCG}$. The simulations imply that high redshift BCGs are dynamically more complex than their low redshift counterparts.
In 1972 H. L. Montgomery announced a remarkable connection between the distribution of the zeros of the Riemann zeta-function and the distribution of eigenvalues of large random Hermitian matrices. Since then a number of startling developments have occurred making this connection more profound. In particular, random matrix theory has been found to be an extremely useful predictive tool in the theory of L-functions. In this article we will try to explain these recent developments and indicate some diretions for future investigations.
We propose a general approach to characterise fluctuations of measured cross sections of nuclear giant resonances. Simulated cross sections are obtained from a particular, yet representative self-energy which contains all information about fragmentations. Using a wavelet analysis, we demonstrate the extraction of time scales of cascading decays into configurations of different complexity of the resonance. We argue that the spreading widths of collective excitations in nuclei are determined by the number of fragmentations as seen in the power spectrum. An analytic treatment of the wavelet analysis using a Fourier expansion of the cross section confirms this principle. A simple rule for the relative life times of states associated with hierarchies of different complexity is given.
The problem of entropy S and baryon number N_B conservation in phase transitions from deconfined phases (QGP and Q) to hadronic matter H is considered. It is shown that standard construction of both first order phase transitions, H-Q as well as Q-QGP implies a discontinuous structure of entropy per baryon S/N_B when crossing phase boundary; this results in impossibility of equilibrium transition from QGP to hadron gas.   We follow the way suggested recently by H. Satz et al. for the same problem concerning direct transition H-QGP. They proposed a modification of bag pressure parameter B_{QGP} by making it dependent on system temperature T and baryon chemical potential mu; this modification has been demonstrated to be sufficient to provide S/N_B conservation.   Here we show that within DPTM such a modification turns out to be necessary and sufficient for bag pressure B_Q in the Q phase only. The DPTM modified in such a way is shown to satisfy equilibrium Gibbs criteria for phase transitions. Location of phase boundaries in $\mu -T$ plane has been demonstrated to be changed but slightly; the modification tells mainly on baryon number density within Q phase. Two alternative descriptions of nucleon-nucleon interaction - the Hard Core Model and the Mean Field Approximation - have been tested; the results for both cases appeared to be similar. All the results are shown to be stable against rather broad variations of model parameters.
Contrary to the expectation arising from the tanglegram Kuratowski theorem of \'E. Czabarka, L.A. Sz\'ekely and S. Wagner [SIAM J. Discrete Math. 31(3): 1732--1750, (2017)], we construct an infinite antichain of planar tanglegrams with respect to the induced subtanglegram partial order. R.E. Tarjan, R. Laver, D.A. Spielman and M. B\'ona, and possibly others, showed that the partially ordered set of finite permutations ordered by deletion of entries contains an infinite antichain, i.e. there exists an infinite collection of permutations, such that none of them contains another as a pattern. Our construction adds a twist to the construction of Spielman and B\'ona [Electr. J. Comb, Vol. 7. N2.]
The properties of artificial isotropic microwave composites which would possess simultaneously negative permittivity and permeability are studied theoretically. Four kinds of composites are considered. Two of them concern media with split-ring resonator particles with different particle arrangements. The other two are realized with Omega particles. An analytical antenna model of the electromagnetic behavior of a split-ring resonator (SRR) is suggested and verified by numerical simulations. Next, material parameters of composite media made with SRR or Omega particles are calculated. It is shown that the Omega-composites are more prospective for obtaining negative real values of permittivity and permeability than the split-ring resonators.
The circumgalactic medium (CGM) is closely linked to galaxy formation and evolution, but difficult to characterize observationally and typically poorly resolved in cosmological simulations. We use spherically-symmetric, idealized, high-resolution simulations of the CGM in $10^{12}M_\odot$ and $10^{11}M_\odot$ dark matter halos to characterize the gas pressure, turbulent and radial velocities, and degree of thermal and effective dynamic pressure support in the overall CGM as well as in its high- and low-temperature phases. We find that the $10^{12}M_\odot$ halo contains a CGM mostly formed of a hot gas halo in hydrostatic equilibrium out of which cold gas condenses and falls onto the central galaxy, while the $10^{11}M_\odot$ halo's CGM is not in hydrostatic equilibrium, has a wider spread of properties at a given galactocentric radius, does not have a clear separation of hot and cold phases, and is dominated by bulk motions. We also find that the degree of pressure support in the $10^{11}M_\odot$ halo is strongly dependent on the parameters of the galactic winds of the central galaxy. These results promote the idea that there is no "average" CGM and care must be taken when setting the initial conditions for a small-box simulation of a patch of the CGM.
We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In mapping the transformed exactly solvable D-dimensional ($D\geq 2$) Schr\"{o}dinger equation with constant mass into the effective mass equation by employing a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.
We give a direct proof of the fact that the $L^{p)$-norms of global solutions of the Boussinesq system in $R^{3}$ grow large as $ t \rightarrow + \infty $ for $ 1 < p < 3 $ and decay to zero for $ 3 < p \leq \infty $, providing exact estimates from below and above using a suitable decomposition of the space-time space $ R^{+} \times R^{3} $. In particular, the kinetic energy blows up as $ \| u(t) \|_{2}^{2} \sim c t^{1/2} $ for large time. This contrasts with the case of the Navier-Stokes equations.
Kopparty and Wang studied in [3] the relation between the roots of a univariate polhynomial over GF(q) and the zero-nonzero pattern of its coefficients. We generalize their results to polynomials in more variables.
We study the interplay of topological bottlenecks and energetic barriers to equilibration in a Coulomb spin liquid where a short-range energetic coupling between defects charged under an emergent gauge field supplements their entropic long-range Coulomb interaction. This work is motivated by the prevalence of memory effects observed across a wide range of geometrically frustrated magnetic materials, possibly including the spontaneous Hall effect observed in Pr2Ir2O7. Our model is canonical spin-ice model on the pyrochlore lattice, where farther-neighbour spin couplings give rise to a nearest-neighbor interaction between topological defects which can easily be chosen to be unnatural or not, i.e. attractive or repulsive between defects of equal gauge charge. Among the novel features of this model are the following. After applying a field quench, a rich dynamical approach to equilibrium emerges, dominated by multi-scale energy barriers responsible for long-lived magnetization plateaux. These even allow for the metastability of a "fragmented" spin liquid, an elusive regime where partial order co-exists with a spin liquid. Perhaps most strikingly, the attraction produces clusters of defects whose stability is due to a combination of energetic barriers for their break-up and proximity of opposite charges along with an entropic barrier generated by the topological requirement of annihilating a defect only together with an oppositely charged counterpart. These clusters may take the form of a "jellyfish" spin texture, comprising an arrangement of same-sign gauge-charges, centered on a hexagonal ring with branches of arbitrary length. The ring carries a clockwise or counterclockwise circular flow of magnetisation. This emergent toroidal degrees of freedom provides a possibility for time reversal symmetry breaking with possible relevance to the spontaneous Hall effect observed in Pr2Ir2O7.
We show that correlated dynamics and long time memory persist in self-organized criticality (SOC) systems even when forced away from the defined critical point that exists at vanishing drive strength. These temporal correlations are found for all levels of external forcing as long as the system is not overdriven. They arise from the same physical mechanism that produces the temporal correlations found at the vanishing drive limit, namely the memory of past events stored in the system profile. The existence of these correlations contradicts the notion that a SOC time series is simply a random superposition of events with sizes distributed as a power law, as has been suggested by previous studies.
In earlier works, we had shown that the observed soft lags and r.m.s versus energy of the lower kHz QPO of neutron star binaries can be explained in the framework of a thermal Comptonization model. It was also shown that such an interpretation can provide estimates of the size and geometry of the Comptonizing medium. Here we study the dependence of these estimates on the time-averaged spectral model assumed and on the frequency of the QPO. We use the high quality time lag and r.m.s obtained during March 3rd 1996 observation of 4U 1608-52 by RXTE as well as other observations of the source at different QPO frequencies where a single time-lag between two broad energy bands have been reported. We compare the results obtained when assuming that the time-averaged spectra are represented by the spectrally degenerate "hot" and "cold" seed photon spectral models. We find that for the "hot" seed photon model the medium size is in the range of 0.3-2.0 kms and the size decreases with increasing QPO frequency. On the other hand for the "cold" seed photon model the range for the sizes are much larger 0.5-20 kms and hence perhaps show no variation with QPO frequency. Our results emphasis the need for broad band spectral information combined with high frequency timing to lift this degeneracy. We further show that the r.m.s as a function of energy for the upper kHz QPO is similar to the lower one and indeed we find that the driver for this QPO should be temperature variations of the corona identical to the lower kHz QPO. However, the time lag reported for the upper kHz QPO is hard, which if confirmed, would challenge the simple Comptonization model presented here. It would perhaps imply that reverberation lags are also important and/or the dominate spectral component is not a single temperature medium but a multi-temperature complex one.
The \emph{total graph} $T(G)$ of a multigraph $G$ has as its vertices the set of edges and vertices of $G$ and has an edge between two vertices if their corresponding elements are either adjacent or incident in $G$. We show that if $G$ has maximum degree $\Delta(G)$, then $T(G)$ is $(2\Delta(G)-1)$-choosable. We give a linear-time algorithm that produces such a coloring. The best previous general upper bound for $\Delta(G) > 3$ was $\floor{\frac32\Delta(G)+2}$, by Borodin et al. When $\Delta(G)=4$, our algorithm gives a better upper bound. When $\Delta(G)\in\{3,5,6\}$, our algorithm matches the best known bound. However, because our algorithm is significantly simpler, it runs in linear time (unlike the algorithm of Borodin et al.).