ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present an ab initio theory of the Gilbert damping in substitutionally disordered ferromagnetic alloys. The theory rests on introduced nonlocal torques which replace traditional local torque operators in the well-known torque-correlation formula and which can be formulated within the atomic-sphere approximation. The formalism is sketched in a simple tight-binding model and worked out in detail in the relativistic tight-binding linear muffin-tin orbital (TB-LMTO) method and the coherent potential approximation (CPA). The resulting nonlocal torques are represented by nonrandom, non-site-diagonal and spin-independent matrices, which simplifies the configuration averaging. The CPA-vertex corrections play a crucial role for the internal consistency of the theory and for its exact equivalence to other first-principles approaches based on the random local torques. This equivalence is also illustrated by the calculated Gilbert damping parameters for binary NiFe and FeCo random alloys, for pure iron with a model atomic-level disorder, and for stoichiometric FePt alloys with a varying degree of L10 atomic long-range order.
We present an explicit construction of the factorization of Seiberg-Witten curves for N=2 theory with fundamental flavors. We first rederive the exact results for the case of complete factorization, and subsequently derive new results for the case with breaking of gauge symmetry U(Nc) to U(N1)xU(N2). We also show that integrality of periods is necessary and sufficient for factorization in the case of general gauge symmetry breaking. Finally, we briefly comment on the relevance of these results for the structure of N=1 vacua.
We construct the field of an arbitrarily accelerating and rotating point mass which specializes to the Kerr solution when the acceleration vanishes and specializes to Kinnersley's arbitrarily accelerating point mass when the rotation vanishes.
The mass-metallicity relation shows that the galaxies with the lowest mass have the lowest metallicities. As most dwarf galaxies are in group environments, interaction effects such as tides could contribute to this trend. We perform a series of smoothed particle hydrodynamics (SPH) simulations of dwarf galaxies in external tidal fields to examine the effects of tides on their metallicities and metallicity gradients. In our simulated galaxies, gravitational instabilities drive gas inwards and produce centralized star formation and a significant metallicity gradient. Strong tides can contribute to these instabilities, but their primary effect is to strip the outer low-metallicity gas, producing a truncated gas disk with a large metallicity. This suggests that the role of tides on the mass-metallicity relation is to move dwarf galaxies to higher metallicities.
Traditional semantic segmentation requires a large labeled image dataset and can only be predicted within predefined classes. To solve this problem, few-shot segmentation, which requires only a handful of annotations for the new target class, is important. However, with few-shot segmentation, the target class data distribution in the feature space is sparse and has low coverage because of the slight variations in the sample data. Setting the classification boundary that properly separates the target class from other classes is an impossible task. In particular, it is difficult to classify classes that are similar to the target class near the boundary. This study proposes the Interclass Prototype Relation Network (IPRNet), which improves the separation performance by reducing the similarity between other classes. We conducted extensive experiments with Pascal-5i and COCO-20i and showed that IPRNet provides the best segmentation performance compared with previous research.
We discuss the requirements of good statistics for quantifying non-Gaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes incompatible. It is shown that the first of these requirements prefers a real space (or wavelet) formulation, whereas the latter favours quantities defined in Fourier space. Bearing this in mind we decide to be eclectic and define two new sets of statistics to quantify the level of non-Gaussianity. Both sets make use of the concept of cumulants of a distribution. However, one set is defined in real space, with reference to the wavelet transform, whereas the other is defined in Fourier space. We derive a series of properties concerning these statistics for a Gaussian random field and show how one can relate these quantities to the higher order moments of temperature maps. Although our frameworks lead to an infinite hierarchy of quantities we show how cosmic variance and experimental constraints give a natural truncation of this hierarchy. We then focus on the real space statistics and analyse the non-Gaussian signal generated by points sources obscured by large scale Gaussian fluctuations. We conclude by discussing the practical implementations of these techniques.
This study examines the influence of the fourth generation quarks on the double lepton polarizations forward--backward asymmetries in B \rar K^\ast \ell^+ \ell^- decay. We obtain that for both (muon, tau) channels the magnitude and the sign of the differential forward--backward asymmetries and the magnitude of the average forward--backward asymmetries are quite sensitive to the 4th generation quarks mass and mixing parameters. It can serve as a good tool to search for new physics effects, precisely, to search for the fourth generation quarks(t', b') via its indirect manifestations in the loop diagrams.
In a homogenous and isotropic cosmology, we introduce general exact solutions for some modified gravity models. In particular, we introduce exact solutions for power-law $f(R)$ gravity and Brans-Dicke theory in Einstein and Jordan conformal frames. In the Brans-Dicke case, the solutions are presented for both single and double exponential potentials in Einstein frame which correspond to power-law potentials in Jordan frame. Our analysis for extracting general exact solutions can also be generalized to those scalar-tensor theories in which the scalar field has an exponential coupling to Ricci scalar.
We show that the $N=2$ and $N=4$ SUSY Yang-Mills action can be reformulated in the sense of non-commutative geometry on $M^4\times (Z_2\oplus Z_2)$ in a rather simple way. In this way the scalars or pseudoscalars are viewed as gauge fields along two directions in the space of one-forms on $Z_2\oplus Z_2$.
We elaborate on a novel superconformal mechanics model possessing D(2,1;alpha) symmetry and involving extra U(2) spin variables. It is the one-particle case of the N=4 superconformal matrix model recently proposed in arXiv:0812.4276 [hep-th], and it generalizes to arbitrary alpha\neq0 the OSp(4|2) superconformal mechanics of arXiv:0905.4951 [hep-th]. As in the latter case, the U(2) spin variables are described by a Wess-Zumino action and define the first Hopf map S^3 -> S^2 in the target space. Upon quantization, they represent a fuzzy sphere. We find the classical and quantum generators of the D(2,1;alpha) superalgebra and their realization on the physical states. The super wavefunction encompasses various multiplets of the SU(2)_R and SU(2)_L subgroups of D(2,1;alpha), with fixed isospins. The conformal potential is determined by the external magnetic field in the Wess-Zumino term, whose amplitude is quantized like in the OSp(4|2) case. As a byproduct, we reveal new invariant subspaces in the enveloping algebra of D(2,1;alpha) for our quantum realization.
A one parameter family of static charged black hole solutions in $(2+1)$-dimensional general relativity minimally coupled to a dilaton $\phi\propto ln({r\over\beta})$ with a potential term $e^{b\phi}\Lambda$ is obtained. Their causal strutures are investigated, and thermodynamical temperature and entropy are computed. One particular black hole in the family has the same thermodynamical properties as the Schwarzschild black hole in $3+1$ dimensions. Solutions with cosmological horizons are also discussed. Finally, a class of black holes arising from the dilaton with a negative kinetic term (tachyon) is briefly discussed.
We study the circumstellar environment of the carbon-rich star R Scl using the near- and mid-infrared high spatial resolution observations from the ESO-VLTI instruments VINCI and MIDI. These observations aim at increasing our knowledge of the dynamic processes in play within the very close circumstellar environment where the mass loss of AGB stars is initiated. Data are interpreted using a self-consistent dynamic model. Interferometric observations do not show any significant variability effect at the 16 m baseline between phases 0.17 and 0.23 in the K band, and for both the 15 m baseline between phases 0.66 and 0.97 and the 31 m baseline between phases 0.90 and 0.97 in the N band. We find fairly good agreement between the dynamic model and the spectrophotometric data from 0.4 to 25 $\mu$m. The model agrees well with the time-dependent flux data at 8.5 $\mu$m, whereas it is too faint at 11.3 and 12.5 $\mu$m. The VINCI visibilities are reproduced well, meaning that the extension of the model is suitable in the K-band. In the mid-infrared, the model has the proper extension to reveal molecular structures of C2H2 and HCN located above the stellar photosphere. However, the windless model used is not able to reproduce the more extended and dense dusty environment. Among the different explanations for the discrepancy between the model and the measurements, the strong nonequilibrium process of dust formation is one of the most probable. The complete dynamic coupling of gas and dust and the approximation of grain opacities with the small-particle limit in the dynamic calculation could also contribute to the difference between the model and the data.
The integrated HydroKinetic Model (iHKM) is applied to analyse the results of direct photon spectra as well as elliptic and triangular flow measurements in 200A GeV Au+Au collisions at RHIC for different centrality bins. Experiments detect the strong centrality dependence of photon elliptic and triangular flow as increasing $v_n(p_T)$-coefficients towards peripheral collisions. The photon production in the model is accumulated from the different sources along with the process of relativistic heavy ion collision developing. Those include the primary hard photons from the parton collisions at the very early stage of the process, the photons generated at the pre-thermal phase of dense matter evolution, then thermal photons at partially equilibrated hydrodynamic quark-gluon stage, together with radiation displaying a confinement and, finally, from the hadron gas phase. Along the way a hadronic medium evolution is treated in two distinct, in a sense opposite, approaches: chemically equilibrium and chemically non-equilibrium, namely, chemically frozen expansion. We find the description of direct photon spectra, elliptic and triangular flow are significantly improved, similar to that found in iHKM for the LHC energies, if an additional portion of photon radiation associated with the confinement processes, the "hadronization photons", is included into consideration.
The transport properties of domain walls in oxygen deficient multiferroic YMnO3 single crystals have been probed using conductive atomic force microscopy and piezoresponse force microscopy. Domain walls exhibit significantly enhanced conductance after being poled in electric fields, possibly induced by oxygen vacancy ordering at domain walls. The electronic conduction can be understood by the Schottky emission and Fowler-Nordheim tunnelling mechanisms. Our results show that the domain wall conductance can be modulated through band structure engineering by manipulating ordered oxygen vacancies in the poling fields.
Given two graphs $H_1$ and $H_2$, a graph is $(H_1,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ or $H_2$. Let $P_t$ and $C_t$ be the path and the cycle on $t$ vertices, respectively. A bull is the graph obtained from a triangle with two disjoint pendant edges. In this paper, we show that there are finitely many 5-vertex-critical ($P_5$,bull)-free graphs.
An approach to pairing in finite nuclei at nonzero temperature is proposed, which incorporates the effects due to the quasiparticle-number fluctuation (QNF) around Bardeen-Cooper-Schrieffer (BCS) mean field and dynamic coupling to quasiparticle-pair vibrations within the self-consistent quasiparticle random-phase approximation (SCQRPA). The numerical calculations of pairing gap, total energy, and heat capacity were carried out within a doubly folded multilevel model as well as realistic nuclei $^{56}$Fe and $^{120}$Sn. The results obtained show that, under the effect of QNF, in the region of moderate and strong couplings, the sharp transition between the superconducting and normal phases is smoothed out, resulting in a thermal pairing gap, which does not collapse at the BCS critical temperature, but has a tail, which extends to high temperature. The dynamic coupling of quasiparticles to SCQRPA vibrations significantly improves the agreement with the results of exact calculations and those obtained within the finite-temperature quantal Monte Carlo method for the total energy and heat capacity. It also causes a deviation of the quasiparticle occupation numbers from the Fermi-Dirac distributions for free fermions.
We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally) solutions of the Euler equations. It is known that there is a unique possible pressure gradient for these curves whenever their end points are fixed. In addition, this pressure field has a limited but unconditional (internal) regularity. The present paper completes these results by showing: 1) the uniqueness property can be viewed as an infinite dimensional phenomenon (related to the possibility of relaxing the corresponding minimization problem by convex optimization), which is false for finite dimensional configuration spaces such as O(3) for the motion of rigid bodies; 2) the unconditional partial regularity is necessarily limited.
Strongly correlated models on coupled ladders in the presence of frustration, in particular the trellis lattice, are studied by numerical techniques. For the undoped case, the possibility of incommensurate peaks in the magnetic structure factor at low temperatures is suggested. In the doped case, our main conclusion for the trellis lattice is that by increasing the interladder coupling, the balance between the magnetic energy in the ladders and the kinetic energy in the zig-zag chains is altered leading eventually to the destruction of the hole pairs initially formed and localized in the ladders.
Let $G$ be a graph with adjacency matrix $A(G)$ and let $D(G)$ be the diagonal matrix of the degrees of $G$. For any real $\alpha\in [0,1]$, Nikiforov \cite{VN1} defined the matrix $A_{\alpha}(G)$ as $$A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G).$$ In this paper, we give some results on the eigenvalues of $A_{\alpha}(G)$ with $\alpha>1/2$. In particular, we show that for each $e\notin E(G)$, $\lambda_i(A_{\alpha}(G+e))\geq\lambda_i(A_{\alpha}(G))$. By utilizing the result, we prove have $\lambda_k(A_{\alpha}(G))\leq\alpha n-1$ for $2\leq k\leq n$. Moreover, we characterize the extremal graphs with equality holding. Finally, we show that $\lambda_n(A_{\alpha}({G}))\geq 2\alpha-1$ if $G$ contains no isolated vertices.
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic process. Under assumptions on this process, which are satisfied, e.g., by stationary Markov chains on finite sets, by stationary Gibbs measures on finite state spaces, or by Gaussian Markov processes, we show that the limiting spectral distribution depends on the way the matrix is filled with the stochastic process. If the filling is in a certain way compatible with the symmetry condition on the matrix, the limiting law of the empirical eigenvalue distribution is the well known semi-circle law. For other fillings we show that the semi-circle law cannot be the limiting spectral density.
We study the strong and electromagnetic decay properties of scalar mesons above 1 GeV within a chiral approach. The scalar-isoscalar states are treated as mixed states of quarkonia and glueball configurations. A fit to the experimental decay rates listed by the Particle Data group is performed to extract phenomenological constraints on the nature of the scalar resonances. A comparison to other theoretical approaches in the scalar meson sector is discussed.
This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.
We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.
We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to infinity, to the weak solution of an associated McKean-Vlasov equation. We derive a large deviation principle via the weak convergence approach. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under rather mild assumptions and also for models described by SDEs not of diffusion type. To illustrate this, we treat the case of SDEs with delay.
We introduce novel Einstein spaces which are the {\it stationary analogs of de Sitter and ani-de Sitter} spacetimes. Having $\Lambda$ as their only parameter, the inherent anisotropy in these solutions appears as a dilemma if we treat the cosmological term as a constant background curvature. Since the cosmological term is an inseparable element of the current cosmological models, further development of these models as well as resolution of the problems related to this term, including any quantum aspect will crucially depend on the true nature of this term. These solutions, which to the best of our knowledge appear here for the first time in the literature, not only open a new direction to study the cosmological term, but also provide strong evidence in favor of the cosmological term as a dark fluid, hence furnishing a resolution to the above mentioned dilemma.
We construct and discuss a toy model of the population of numerous non-identical extragalactic sources of ultra-high-energy cosmic rays. In the model, cosmic-ray particles are accelerated in magnetospheres of supermassive black holes in galactic nuclei, the key parameter of acceleration being the black-hole mass. We use astrophysical data on the redshift-dependent black-hole mass function to describe the population of these cosmic-ray accelerators, from weak to powerful, and confront the model with cosmic-ray data.
In this paper, we derive eight basic identities of symmetry in three variables related to Bernoulli polynomials and power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interesting ones. The derivations of identities are based on the $p$-adic integral expression of the generating function for the Bernoulli polynomials and the quotient of integrals that can be expressed as the exponential generating function for the power sums.
With the help of computer algebra we study the diagonal matrix elements <Or^p>, where O are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem. Using Zeilberger's extension of Gosper's algorithm and a variant to it, three-term recurrence relations for each of these expectation values are derived together with some transformation formulas for the corresponding generalized hypergeometric series. In addition, the virial recurrence relations for these integrals are also found and proved algorithmically.
For visual manipulation tasks, we aim to represent image content with semantically meaningful features. However, learning implicit representations from images often lacks interpretability, especially when attributes are intertwined. We focus on the challenging task of extracting disentangled 3D attributes only from 2D image data. Specifically, we focus on human appearance and learn implicit pose, shape and garment representations of dressed humans from RGB images. Our method learns an embedding with disentangled latent representations of these three image properties and enables meaningful re-assembling of features and property control through a 2D-to-3D encoder-decoder structure. The 3D model is inferred solely from the feature map in the learned embedding space. To the best of our knowledge, our method is the first to achieve cross-domain disentanglement for this highly under-constrained problem. We qualitatively and quantitatively demonstrate our framework's ability to transfer pose, shape, and garments in 3D reconstruction on virtual data and show how an implicit shape loss can benefit the model's ability to recover fine-grained reconstruction details.
The isotopic composition of beryllium nuclei and its energy dependence encode information of fundamental importance about the propagation of cosmic rays in the Galaxy. The effects of decay on the spectrum of the unstable beryllium--10 isotope can be described introducing the average survival probability $P_{\rm surv} (E_0)$ that can inferred from measurements of the isotopic ratio Be10/Be9 if one has sufficiently good knowledge of the nuclear fragmentation cross sections that determine the isotopic composition of beryllium nuclei at injection. The average survival probability can then be interpreted in terms of propagation parameters, such as the cosmic ray average age, adopting a theoretical framework for Galactic propagation. Recently the AMS02 Collaboration has presented preliminary measurements of the beryllium isotopic composition that extend the observations to a broad energy range ($E_0 \simeq 0.7$-12 GeV/n) with small errors. In this work we discuss the average survival probability that can be inferred from the preliminary AMS02 data, adopting publically available models of the nuclear fragmentation cross sections, and interpret the results in the framework of a simple diffusion model, This study shows that the effects of decay decrease more slowly than the predictions, resulting in an average cosmic ray age that increases with energy. An alternative possibility is that the cosmic ray age distribution is broader than in the models that are now commonly accepted, suggesting that the Galactic confinement volume has a non trivial structure and is formed by an inner halo contained in an extended one.