ShantanuT01/DACTYL-Pretraining huggingface dataset:
Spin-1/2 Ising-Heisenberg model with XYZ Heisenberg pair interaction and two different Ising quartic interactions is exactly solved with the help of the generalized star-square transformation, which establishes a precise mapping equivalence with the corresponding eight-vertex model on a square lattice generally satisfying Baxter's zero-field (symmetric) condition. The investigated model exhibits a remarkable weak-universal critical behavior with two marked wings of critical lines along which critical exponents vary continuously with the interaction parameters. Both wings of critical lines merge together at a very special quantum critical point of the infinite order, which can be characterized through diverging critical exponents. The possibility of observing reentrant phase transitions in a close vicinity of the quantum critical point is related to a relative strength of the exchange anisotropy in the XYZ Heisenberg pair interaction.
We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.
Sampling from a random discrete distribution induced by a `stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons, doubletons, etc) can be read off from a limiting model involving a unit Poisson point process and a self-similar renewal process on the halfline.
We set up the problem of finding the transition state for phase nucleation in multi-component fluid mixtures, within the Landau-Ginzburg density functional. We establish an expression for the coordinate-dependent local pressure that applies to mixtures, arbitrary geometries, and certain non-equilibrium configurations. The expression allows one to explicitly evaluate the pressure in spherical geometry, \`a la van der Waals. Pascal's law is recovered within the Landau-Ginzburg density functional theory, formally analogously to how conservation of energy is recovered in the Lagrangian formulation of mechanics. We establish proper boundary conditions for certain singular functional forms of the bulk free energy density that allow one to obtain droplet solutions with thick walls in essentially closed form. The hydrodynamic modes responsible for mixing near the interface are explicitly identified in the treatment; the composition at the interface is found to depend only weakly on the droplet size. Next we develop a Landau-Ginzburg treatment of the effects of amphiphiles on the surface tension; the amphiphilic action is seen as a violation of Pascal's law. We explicitly obtain the binding potential for the detergent at the interface and the dependence of the down-renormalization of the surface tension on the activity of the detergent. Finally, we argue that the renormalization of the activation barrier for escape from long-lived structures in glassy liquids can be viewed as an action of uniformly seeded, randomly oriented amphiphilic molecules on the interface separating two dissimilar aperiodic structures. This renormalization is also considered as a "wetting" of the interface. The resulting conclusions are consistent with the random first order transition (RFOT) theory.
An etale cohomology group $W$ of some irreducible components, which is the smooth compactification of an affine curve $(X^{q^2}-X)^{q-1}=(Y^{q(q+1)}-Y^{q+1})^{q-1},$ in the stable reduction the Lubin-Tate curve of level two is related to the Lusztig theory over finite rings. In this paper, we investigate a relationship between the cohomology group $W$ and the Lusztig theory.
We analyze the embedded stellar content in the vicinity of the W3/W4/W5 HII regions using the FCRAO Outer Galaxy 12CO(J=1-0) Survey, the IRAS Point Source Catalog, published radio continuum surveys, and new near-infrared and molecular line observations. Thirty-four IRAS Point Sources are identified that have far-infrared colors characteristic of embedded star forming regions, and we have obtained K' mosaics and 13CO(J=1-0) maps for 32 of them. Ten of the IRAS sources are associated with an OB star and 19 with a stellar cluster, although three OB stars are not identified with a cluster. Half of the embedded stellar population identified in the K' images is found in just the 5 richest clusters, and 61% is contained in IRAS sources associated with an embedded OB star. Thus rich clusters around OB stars contribute substantially to the stellar population currently forming in the W3/W4/W5 region. Approximately 39% of the cluster population is embedded in small clouds with an average mass of ~130 Mo that are located as far as 100 pc from the W3/W4/W5 cloud complex. We speculate that these small clouds are fragments of a cloud complex dispersed by previous episodes of massive star formation. Finally, we find that 4 of the 5 known embedded massive star forming sites in the W3 molecular cloud are found along the interface with the W4 HII region despite the fact that most of the molecular mass is contained in the interior regions of the cloud. These observations are consistent with the classical notion that the W4 HII region has triggered massive star formation along the eastern edge of the W3 molecular cloud.
We achieve a detailed understanding of the $n$-sided planar Poisson-Voronoi cell in the limit of large $n$. Let ${p}\_n$ be the probability for a cell to have $n$ sides. We construct the asymptotic expansion of $\log {p}\_n$ up to terms that vanish as $n\to\infty$. We obtain the statistics of the lengths of the perimeter segments and of the angles between adjoining segments: to leading order as $n\to\infty$, and after appropriate scaling, these become independent random variables whose laws we determine; and to next order in $1/n$ they have nontrivial long range correlations whose expressions we provide. The $n$-sided cell tends towards a circle of radius $(n/4\pi\lambda)^{\half}$, where $\lambda$ is the cell density; hence Lewis' law for the average area $A\_n$ of the $n$-sided cell behaves as $A\_n \simeq cn/\lambda$ with $c=1/4$. For $n\to\infty$ the cell perimeter, expressed as a function $R(\phi)$ of the polar angle $\phi$, satisfies $d^2 R/d\phi^2 = F(\phi)$, where $F$ is known Gaussian noise; we deduce from it the probability law for the perimeter's long wavelength deviations from circularity. Many other quantities related to the asymptotic cell shape become accessible to calculation.
The fluorination of mono- and bi-layer graphene have been studied by means of ab-initio DFT calculations. The stability of CF$_x$ systems are found to depend on both the F coverage and on the position of the F atoms regarding the C sublattices. When F atoms is chemisorbed to C atoms belonging to the same sublattice, low coverage is preferred. Otherwise, large F coverable is more stable (up to C$_4$F). The difference of charge distribution between the two carbon sublattices explains this finding that is confirmed by the analysis of the diffusion barriers. Binding energy of F on bi-layer systems is also computed slightly smaller than on monolayer and electronic decoupling is observed when only one of the layer is exposed to fluorine.
The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does in general not satisfy an It\^{o} formula like the solution of a finite-dimensional stochastic ordinary differential equation (SODE). In particular, it is not possible to derive stochastic Taylor expansions as for the solution of a SODE using an iterated application of the It\^{o} formula. Consequently, until recently, only low order numerical approximation results for such a SPDE have been available. Here, the fact that the solution of a SPDE driven by additive noise can be interpreted in the mild sense with integrals involving the exponential of the dominant linear operator in the SPDE provides an alternative approach for deriving stochastic Taylor expansions for the solution of such a SPDE. Essentially, the exponential factor has a mollifying effect and ensures that all integrals take values in the Hilbert space under consideration. The iteration of such integrals allows us to derive stochastic Taylor expansions of arbitrarily high order, which are robust in the sense that they also hold for other types of driving noise processes such as fractional Brownian motion. Combinatorial concepts of trees and woods provide a compact formulation of the Taylor expansions.
We propose a novel architecture for object classification, called Self-Attention Capsule Networks (SACN). SACN is the first model that incorporates the Self-Attention mechanism as an integral layer within the Capsule Network (CapsNet). While the Self-Attention mechanism supplies a long-range dependencies, results in selecting the more dominant image regions to focus on, the CapsNet analyzes the relevant features and their spatial correlations inside these regions only. The features are extracted in the convolutional layer. Then, the Self-Attention layer learns to suppress irrelevant regions based on features analysis and highlights salient features useful for a specific task. The attention map is then fed into the CapsNet primary layer that is followed by a classification layer. The proposed SACN model was designed to solve two main limitations of the baseline CapsNet - analysis of complex data and significant computational load. In this work, we use a shallow CapsNet architecture and compensates for the absence of a deeper network by using the Self-Attention module to significantly improve the results. The proposed Self-Attention CapsNet architecture was extensively evaluated on six different datasets, mainly on three different medical sets, in addition to the natural MNIST, SVHN and CIFAR10. The model was able to classify images and their patches with diverse and complex backgrounds better than the baseline CapsNet. As a result, the proposed Self-Attention CapsNet significantly improved classification performance within and across different datasets and outperformed the baseline CapsNet, ResNet-18 and DenseNet-40 not only in classification accuracy but also in robustness.
A theoretical study of the subpicosecond fragmentation of C60 clusters in response to ultrafast laser pulses is presented. We simulate the laser excitation and the consequent nonequilibrium relaxation dynamics of the electronic and nuclear degrees of freedom. The first stages of the nonequilibrium dynamics are dominated by a coherent breathing mode followed by the cold ejection of single C atoms, in contrast to the dimer emission which characterizes the thermal relaxation. We also determine the nonequilibrium damage thresholds as a function of the pulse duration.
We report the observation of gravitational waves from two compact binary coalescences in LIGO's and Virgo's third observing run with properties consistent with neutron star-black hole (NSBH) binaries. The two events are named GW200105_162426 and GW200115_042309, abbreviated as GW200105 and GW200115; the first was observed by LIGO Livingston and Virgo, and the second by all three LIGO-Virgo detectors. The source of GW200105 has component masses $8.9^{+1.2}_{-1.5}\,M_\odot$ and $1.9^{+0.3}_{-0.2}\,M_\odot$, whereas the source of GW200115 has component masses $5.7^{+1.8}_{-2.1}\,M_\odot$ and $1.5^{+0.7}_{-0.3}\,M_\odot$ (all measurements quoted at the 90% credible level). The probability that the secondary's mass is below the maximal mass of a neutron star is 89%-96% and 87%-98%, respectively, for GW200105 and GW200115, with the ranges arising from different astrophysical assumptions. The source luminosity distances are $280^{+110}_{-110}$ Mpc and $300^{+150}_{-100}$ Mpc, respectively. The magnitude of the primary spin of GW200105 is less than 0.23 at the 90% credible level, and its orientation is unconstrained. For GW200115, the primary spin has a negative spin projection onto the orbital angular momentum at 88% probability. We are unable to constrain spin or tidal deformation of the secondary component for either event. We infer a NSBH merger rate density of $45^{+75}_{-33}\,\mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$ when assuming GW200105 and GW200115 are representative of the NSBH population, or $130^{+112}_{-69}\,\mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$ under the assumption of a broader distribution of component masses.
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
We present a three-dimensional map of the hydrogen density distribution in the Galactic interstellar medium. The hydrogen equivalent column densities were obtained from the Exploring the X-ray Transient and variable Sky project ({\sc EXTraS}) which provides equivalent $N_{\rm H}$ values from X-ray spectral fits of observations within the {\it XMM-Newton} Data Release. {\sc EXTraS} include multiple fits for each source, allowing an accurate determination of the equivalent column densities, which depends on the continuum modeling of the spectra. A cross-correlation between the {\sc EXTraS} catalogue and the first {\it Gaia} Data Release was performed in order to obtain accurate parallax and distance measurements. We use a Bayesian method explained in \citet{rez17} in order to predict the most probable distribution of the density at any arbitrary point, even for lines of sight along which there are no initial observation. The resulting map shows small-scale density structures which can not been modeled by using analytic density profiles. In this paper we present a proof of concept of the kind of science possible with the synergy of these catalogs. However, given the systematic uncertainties connected to the source identification and to the dependence of $N_{\rm H}$ on the spectral model, the present maps should be considered qualitatively at this point.
In this paper we obtain comparison results for the quasilinear equation $-\Delta_{p,x} u - u_{yy} = f$ with homogeneous Dirichlet boundary conditions by Steiner rearrangement in variable $x$, thus solving a long open problem. In fact, we study a broader class of anisotropic problems. Our approach is based on a finite-differences discretization in $y$, and the proof of a comparison principle for the discrete version of the auxiliary problem $A U - U_{yy} \le \int_0^s f^*$, where $AU = (n\omega^{1/n}s^{1/n'} )^p (- U_{ss})^{p-1}$. We show that this operator is T-accretive in $L^\infty$. We extend our results for $-\Delta_{p,x}$ to general operators of the form $-\mathrm{div} (a(|\nabla_x u|) \nabla_x u)$ where $a$ is non-decreasing and behaves like $| \cdot |^{p-2}$ at infinity.
A competitive (2+1)-dimensional model of deposit formation, based on the combination of random sequential absorption deposition (RSAD), ballistic deposition (BD) and random deposition (RD) models, is proposed. This model was named as RSAD$_{1-s}$(RD$_f$BD$_{1-f}$)$_s$. It allows to consider different cases of interparticle interactions from complete repulsion between near-neighbors in the RSAD model ($s=0$) to sticking interactions in the BD model ($s=1, f=0$) or absence of interactions in the RD model ($s=1$, $f=0$). The ideal checkerboard ordered structure was observed for the pure RSAD model ($s=0$) in the limit of $h \to \infty$. Defects in the ordered structure were observed at small $h$. The density of deposit $p$ versus system size $L$ dependencies were investigated and the scaling parameters and values of $p_\infty=p(L=\infty)$ were determined. Dependencies of $p$ versus parameters of the competitive model $s$ and $f$ were studied. We observed the anomalous behaviour of the eposit density $p_\infty$ with change of the inter-particle repulsion, which goes through minimum on change of the parameter $s$. For pure RSAD model, the concentration of defects decreases with $h$ increase in accordance with the critical law $\rho\propto h^{-\chi_{RSAD}}$, where $\chi_{RSAD} \approx 0.119 \pm 0.04$.
Equivariant cohomology is suggested as an alternative algebraic framework for the definition of topological field theories constructed by E. Witten circa 1988. It also enlightens the classical Faddeev Popov gauge fixing procedure.
In 1914, Eddington derived a formula for the difference between the mean absolute magnitudes of stars "in space" or gathered "from the sky". Malmquist (1920) derived a general relation for this difference in Euclidean space. Here we study this statistical bias in cosmology, clarifying and expanding previous work.   We derived the Malmquist relation within a general cosmological framework, including Friedmann's model, analogously to the way Malmquist showed in 1936 that his formula is also valid in the presence of extinction in Euclidean space. We also discuss some conceptual aspects that explain the wide scope of the bias relation.   The Malmquist formula for the intrinsic difference <M>_m - M_0 = - sigma_M^2 dlna(m)/dm is also valid for observations made in an expanding Friedmann universe. This is holds true for bolometric and finite-band magnitudes when a(m) refers to the distribution of observed (uncorrected for K-effect or z-dependent extinction) apparent magnitudes.
We have calculated optical conductivity [$\sigma(\omega)$] spectra of ytterbium compounds (YbAl$_3$, YbAl$_2$, YbCu$_2$Si$_2$, YbNi$_2$Ge$_2$, YbInCu$_4$, YbRh$_2$Si$_2$, YbIr$_2$Si$_2$, and YbB$_{12}$) based on the direct interband transition derived from first-principle band calculation and compared the results with the experimentally obtained $\sigma(\omega)$ spectra. The spectral feature of a peak in the middle-infrared region (mid-IR peak) and a shoulder structure in the far-infrared region (far-IR shoulder) in the experimental $\sigma(\omega)$ spectra can be described by the band calculation with a common renormalization factor. This result indicates that the infrared spectra of Yb compounds originate from the interband transition from the Yb $4f$ state but that the Yb $4f$ state shifts to the Fermi level with strong electron correlation.
We calculate the leading order corrections (in $r_s$) to the static polarization $\Pi^{*}(q,0,)$, with dynamically screened interactions, for the two-dimensional electron gas. The corresponding diagrams all exhibit singular logarithmic behavior in their derivatives at $q=2 k_F$ and provide significant enhancement to the proper polarization particularly at low densities. At a density of $r_s=3$, the contribution from the leading order {\em fluctuational} diagrams exceeds both the zeroth order (Lindhard) response and the self-energy and exchange contributions. We comment on the importance of these diagrams in two-dimensions and make comparisons to an equivalent three-dimensional electron gas; we also consider the impact these finding have on $\Pi^{*}(q,0)$ computed to all orders in perturbation theory.
Let p be an odd prime number. In this paper, we show existence of certain infinite families of imaginary quadratic fields in which p splits and whose Iwasawa {\lambda}-invariant of the cyclotomic Zp-extension is equal to 1.
The effect of isospin breaking pion s-wave rescattering is included in elastic NN scattering at low energies using effective field theory. Although this mechanism gave a large contribution to charge symmetry breaking in np --> d pi0, the effect is rather small in pp vs. nn scattering parameters and in the 3H-3He binding energy difference. This smallness is caused by large cancellation of the up-down quark mass difference contribution and electromagnetic effects to the np mass difference.
The free action for the massless sector of the Type II superstring was recently constructed using closed RNS superstring field theory. The supersymmetry transformations of this action are shown to satisfy an N=2 D=10 SUSY algebra with Ramond-Ramond central charges.
We develop a new semi-dynamical method to study shock revival by neutrino heating in core- collapse supernovae. Our new approach is an extension of the previous studies that employ spherically symmetric, steady, shocked accretion flows together with the light bulb approximation. The latter has been widely used in the supernova community for the phenomenological investigation of the criteria for successful supernova explosions. In the present approach, on the other hand, we get rid of the steady-state condition and take into account shock wave motions instead. We have in mind the scenario that not the critical luminosity but the critical fluctuation generated by hydrodynamical instabilities such as SASI and neutrino-driven convection in the post-shock region determines the onset of shock revival. After confirming that the new approach indeed captures the dynamics of revived shock wave qualitatively, we then apply the method to various initial conditions and find that there is a critical fluctuation for shock revival, which can be well fit by the following formula: f_crit ~ 0.8 * (M_in/1.4M_sun) * {1- (rsh/10^8cm)}, in which fcrit denotes the critical pressure fluctuation normalized by the unperturbed post-shock value. Min and rsh stand for the mass of the central compact object and the shock radius, respectively. The critical fluctuation decreases with the shock radius, whereas it increases with the mass of the central object. We discuss the possible implications of our results for 3D effects on shock revival, which is currently controversial in the supernova community.
We propose purely electric manipulation of spin qubits by means of the spin-orbit interaction (SOI) {\it without magnetic field or magnets} in a double-quantum dot. All the unitary transformations can be constructed by the time-dependent Dzyaloshinsky-Moriya interaction between the two spins, which arises from the Rashba SOI modulated by electric field. As a few demonstrations, we study both analytically and numerically the three operations, i.e., (A) the spin initialization, (B) the two-spin rotation in the opposite directions, and (C) the two-spin rotation in the same direction. The effects of the relaxation and the feasibility of this proposal are also discussed.
We construct gravitational solutions that holographically describe two different $d=4$ SCFTs joined together at a co-dimension one, planar RG interface and preserving $d=3$ superconformal symmetry. The RG interface joins $\mathcal{N}=4$ SYM theory on one side with the $\mathcal{N}=1$ Leigh-Strassler SCFT on the other. We construct a family of such solutions, which in general are associated with spatially dependent mass deformations on the $\mathcal{N}=4$ SYM side, but there is a particular solution for which these deformations vanish. We also construct a Janus solution with the Leigh-Strassler SCFT on either side of the interface. Gravitational solutions associated with superconformal interfaces involving ABJM theory and two $d=3$ $\mathcal{N}=1$ SCFTs with $G_2$ symmetry are also discussed and shown to have similar properties, but they also exhibit some new features.