ShantanuT01/DACTYL-Pretraining huggingface dataset:
A relation between O$(n)$ models and Ising models has been recently conjectured [L. Casetti, C. Nardini, and R. Nerattini, Phys. Rev. Lett. 106, 057208 (2011)]. Such a relation, inspired by an energy landscape analysis, implies that the microcanonical density of states of an O$(n)$ spin model on a lattice can be effectively approximated in terms of the density of states of an Ising model defined on the same lattice and with the same interactions. Were this relation exact, it would imply that the critical energy densities of all the O$(n)$ models (i.e., the average values per spin of the O$(n)$ Hamiltonians at their respective critical temperatures) should be equal to that of the corresponding Ising model; it is therefore worth investigating how different the critical energies are and how this difference depends on $n$.   We compare the critical energy densities of O$(n)$ models in three dimensions in some specific cases: the O$(1)$ or Ising model, the O$(2)$ or $XY$ model, the O$(3)$ or Heisenberg model, the O$(4)$ model and the O$(\infty)$ or spherical model, all defined on regular cubic lattices and with ferromagnetic nearest-neighbor interactions. The values of the critical energy density in the $n=2$, $n=3$, and $n=4$ cases are derived through a finite-size scaling analysis of data produced by means of Monte Carlo simulations on lattices with up to $128^3$ sites. For $n=2$ and $n=3$ the accuracy of previously known results has been improved. We also derive an interpolation formula showing that the difference between the critical energy densities of O$(n)$ models and that of the Ising model is smaller than $1\%$ if $n<8$ and never exceeds $3\%$ for any $n$.
An analysis of the position angles distribution of 10461 extended radio sources shows that the spatial orientation of the axes of these objects is anisotropic: they avoid the direction towards the Celestial Pole and are mostly oriented in the equatorial direction. The ratio of the probability densities of the orientation in these two directions is 0.68. The probability that the sky distribution of axes is isotropic is less then 0.00004. This conclusion is consistent with the results of the analyses of the spatial distribution of galactic normals orientation in the galaxies from UGC, ESO and FGC catalogs
In view of Ehlers-Pirani-Schild formalism, since 1972 Weyl geometries should be considered to be the most appropriate and complete framework to represent (relativistic) gravitational fields. We shall here show that in any given Lorentzian spacetime (M,g) that admits global timelike vector fields any such vector field u determines an essentially unique Weyl geometry ([g], \Gamma) such that u is \Gamma-geodesic (i.e. parallel with respect to \Gamma).
We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks we consider satisfy the so-called complete resource pooling condition and therefore have one-dimensional approximating Brownian control problems.   We propose a simple discrete review policy for controlling such networks.   Assuming 2+\epsilon moments on the interarrival times and processing times, we provide a conceptually simple proof of asymptotic optimality of the proposed policy.
At the age of about 1 year, the spectra of most Type Ia supernovae are dominated by strong forbidden nebular emission lines of FeII and FeIII. Later observations (at about 2 years) of the nearby SN 2011fe showed an unexpected shift of ionization to FeI and FeII. Spectra of the very nearby SN Ia 2014J at an intermediate phase (1 - 1.5 years) that are presented here show a progressive decline of FeIII emission, while FeI is not yet strong. The decrease in ionization can be explained if the degree of clumping in the ejecta increases significantly at ~1.5 years, at least in the Fe-dominated zone. Models suggest that clumps remain coherent after about one year, behaving like shrapnel. The high density in the clumps, combined with the decreasing heating rate, would then cause recombination. These data may witness the phase of transition from relatively smooth ejecta to the very clumpy morphology that is typical of SN remnants. The origin of the increased clumping may be the development of local magnetic fields.
We present a new class of multifractal process on R, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the boundaries of multitype Galton-Watson trees. Our class of processes includes Brownian motion subjected to a continuous multifractal time-change. In addition, if we observe our process at a fixed spatial resolution, then we can obtain a finite Markov representation of it, which we can use for on-line simulation. That is, given only the Markov representation at step n, we can generate step n+1 in O(log n) operations. Detailed pseudo-code for this algorithm is provided.
Melting of MgO was studied using a multicanonical ensemble method combined with a first-principles calculation. This approach has been successively performed by using a rather simple functional form for a model inter-atomic potential that is determined from first-principles and a novel approximation treating auxiliary degrees of freedom, such as electron thermal excitations, within a multicanonical ensemble method. Although a rather simple model potential was used, this approach could distinguish differences due to the exchange-correlation potential used in the first-principles calculations. The pressure dependence of the melting point, latent heat, and volume change during melting were studied. The obtained dependence was similar to that reported by Alfe which differs from experimental results. This dependence did not change even with the PBEsol exchange-correlation potential.
We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT$_4$ proposed by \"{O}.G\"{u}rdo\u{g}an and one of the authors as a double scaling limit of $\gamma$-deformed $\mathcal{N}=4$ SYM theory. We give full description of bulk behavior of large Feynman graphs: it shows a generalized "dynamical fishnet" structure, with a dynamical exchange of bosonic and Yukawa couplings. We compute certain four-point correlators in the full chiral CFT$_4$, generalizing recent results for a particular one-coupling version of this theory -- the bi-scalar "fishnet" CFT. We sum up exactly the corresponding Feynman diagrams, including both bosonic and fermionic loops, by Bethe-Salpeter method. This provides explicit OPE data for various twist-2 operators with spin, showing a rich analytic structure, both in coordinate and coupling spaces.
We study and classify up to a linear conjugation germs of flows in the space of quadratic birational transformations of the complex projective space of dimension 3. As a consequence we show that every quadratic flow preserves a pencil of planes through a line.
We consider the cubic Nonlinear Schrodinger Equation in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time H^s bounds in terms of the H^s size of the initial data for s greater than or equal to -1/6.
For a smooth complex projective variety, the rank of the N\'eron-Severi group is bounded by the Hodge number h^{1,1}. Varieties with rk NS = h^{1,1} have interesting properties, but are rather sparse, particularly in dimension 2. We discuss in this note a number of examples, in particular those constructed from curves with special Jacobians.
We present a general class of exact solutions in Einstein-Maxwell-dilaton gravity describing configurations of black holes and Kaluza-Klein bubbles magnetized along the compact dimension. Smarr-like relations for the mass and the tension are found. We also derive the mass and tension first law for the configurations under consideration using the Noether current approach. The solutions we consider are explicit examples showing that in Kaluza-Klein spacetimes the interval (rod) structure and the charges (which are zero by construction for the solutions here), are insufficient to classify the solutions and additional data is necessary, namely the magnetic flux(es).
The electronic and the structural properties of two dimensional van der Waals metal/semiconductor heterostructures have been investigated through first-principles calculations. We have considered the recently synthesized borophene [Science {\bf 350}, 1513 (2015)], and the planar boron sheets (S1 and S2) [Nature Chemistry {\bf 8}, 563 (2016)] as the 2D metal layer, and the transition metal dichalcogenides (TMDCs) \mose, and \wse\ as the semiconductor monolayer. We find that the energetic stability of those 2D metal/semiconductor heterojunctions is mostly ruled by the vdW interactions; however, chemical interactions also take place in borophene/TMDC. The electronic charge transfers at the metal/semiconductor interface has been mapped, where we find a a net charge transfer from the TMDCs to the boron sheets. Further electronic structure calculations reveal that the metal/semiconductor interfaces, composed by planar boron sheets S1 and S2, present a p-type Schottky barrier which can be tuned to a p-type ohmic contact upon an external electric field.
Observational efforts to image the immediate environment of a black hole at the scale of the event horizon benefit from the development of efficient imaging codes that are capable of producing synthetic data, which may be compared with observational data. We aim to present RAPTOR, a new public code that produces accurate images, animations, and spectra of relativistic plasmas in strong gravity by numerically integrating the equations of motion of light rays and performing time-dependent radiative transfer calculations along the rays. The code is compatible with any analytical or numerical spacetime. It is hardware-agnostic and may be compiled and run both on GPUs and CPUs. We describe the algorithms used in RAPTOR and test the code's performance. We have performed a detailed comparison of RAPTOR output with that of other radiative-transfer codes and demonstrate convergence of the results. We then applied RAPTOR to study accretion models of supermassive black holes, performing time-dependent radiative transfer through general relativistic magneto-hydrodynamical (GRMHD) simulations and investigating the expected observational differences between the so-called fast-light and slow-light paradigms. Using RAPTOR to produce synthetic images and light curves of a GRMHD model of an accreting black hole, we find that the relative difference between fast-light and slow-light light curves is less than 5%. Using two distinct radiative-transfer codes to process the same data, we find integrated flux densities with a relative difference less than 0.01%. For two-dimensional GRMHD models, such as those examined in this paper, the fast-light approximation suffices as long as errors of a few percent are acceptable. The convergence of the results of two different codes demonstrates that they are, at a minimum, consistent.
We study the $\lambda \phi^4$ field theory in a flat Robertson-Walker space-time using the functional Sch\"odinger picture. We introduce a simple Gaussian approximation to analyze the time evolution of pure states and we establish the renormalizability of the approximation. We also show that the energy-momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations.
The search for new interactions and particles in high-energy collider physics relies on precise background predictions. This has led to many advances in combining precise fixed-order cross-section calculations with detailed event generator simulations. In recent years, fixed-order QCD calculations of inclusive cross sections at N3LO precision have emerged, followed by an impressive progress at producing differential results. Once differential results become publicly available, it would be prudent to embed these into event generators to allow the community to leverage these advances. This note offers some concrete thoughts on ME+PS matching at third order in QCD. As a method for testing these thoughts, a toy calculation of $e^+e^-\rightarrow u \bar u$ at $\mathcal{O}(\alpha_s^3)$ is constructed, and combined with an event generator through unitary matching. The toy implementation may serve also as blueprint for high-precision QCD predictions at future lepton colliders. As a byproduct of the N3LO matching formula, a new NNLO+PS formula for processes with "additional" jets is obtained.
We study the properties of convex functionals which have been proposed for the simulation of charged molecular systems within the Poisson-Boltzmann approximation. We consider the extent to which the functionals reproduce the true fluctuations of electrolytes and thus the one-loop correction to mean field theory -- including the Deby-H\"uckel correction to the free energy of ionic solutions. We also compare the functionals for use in numerical optimization of a mean field model of a charged polymer and show that different functionals have very different stiffnesses leading to substantial differences in accuracy and speed.
The question if conserved currents can be sensibly defined in supersymmetric minisuperspaces is investigated in this essay. The objective is to employ exclusively the differential equations obtained {\em directly} from the Lorentz and supersymmetry quantum constraints. The ``square-root'' structure of N=1 supergravity is the motivation to contemplate this tempting idea. However, it is shown that such prospect is not feasible but for some very simple scenarios. Otherwise, conserved currents (and consistent probability densities) can be derived from subsequent Wheeler-DeWitt like equations obtained from the supersymmetric algebra of constraints.
The interaction of an ensemble of $N$ two-level atoms with a single mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by $g_N = \sqrt{N} \bar{g}_1$, where $\bar{g}_1$ is the ensemble-averaged single-atom coupling strength. Formerly, this model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into non-cavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive atoms. We show that the predictions of our model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.
The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency e.g. to aggregate, flock or disperse. The paper examines the kinetic Cucker-Smale equation with a singular communication weight. Given a compactly supported measure as an initial datum we construct a global in time weak measure-valued solution in the space $C_{weak}(0,\infty;\mathcal{M})$. The solution is defined as a mean-field limit of the empirical distributions of particles, which dynamics is governed by the Cucker-Smale particle system. The studied communication weight is $\psi(s)=|s|^{-\alpha}$ with $\alpha \in (0,\frac 12)$. This range of singularity admits sticking of characteristics/trajectories. The second result concerns the weak--atomic uniqueness property stating that a weak solution initiated by a finite sum of atoms, i.e. Dirac deltas in the form $m_i \delta_{x_i} \otimes \delta_{v_i}$, preserves its atomic structure. Hence they coincide with unique solutions to the system of ODEs associated with the Cucker-Smale particle system.
Boron nitride is a promising material for nanotechnology applications due to its two-dimensional graphene-like, insulating, and highly-resistant structure. Recently it has received a lot of attention as a substrate to grow and isolate graphene as well as for its intrinsic UV lasing response. Similar to carbon, one-dimensional boron nitride nanotubes (BNNTs) have been theoretically predicted and later synthesised. Here we use first principles simulations to unambiguously demonstrate that i) BN nanotubes inherit the highly efficient UV luminescence of hexagonal BN; ii) the application of an external perpendicular field closes the electronic gap keeping the UV lasing with lower yield; iii) defects in BNNTS are responsible for tunable light emission from the UV to the visible controlled by a transverse electric field (TEF). Our present findings pave the road towards optoelectronic applications of BN-nanotube-based devices that are simple to implement because they do not require any special doping or complex growth.
Recent applications pose requirements of both cross-domain knowledge transfer and model compression to machine learning models due to insufficient training data and limited computational resources. In this paper, we propose a new knowledge distillation model, named Spirit Distillation (SD), which is a model compression method with multi-domain knowledge transfer. The compact student network mimics out a representation equivalent to the front part of the teacher network, through which the general knowledge can be transferred from the source domain (teacher) to the target domain (student). To further improve the robustness of the student, we extend SD to Enhanced Spirit Distillation (ESD) in exploiting a more comprehensive knowledge by introducing the proximity domain which is similar to the target domain for feature extraction. Results demonstrate that our method can boost mIOU and high-precision accuracy by 1.4% and 8.2% respectively with 78.2% segmentation variance, and can gain a precise compact network with only 41.8% FLOPs.
In this survey we add two new results that are not in our paper [MR15]. Using the idea of brane actions discovered by Toen, we construct a lax associative action of the operad of stable curves of genus zero on a smooth variety X seen as an object in correspondences in derived stacks. This action encodes the Gromov-Witten theory of X in purely geometrical terms.
Motivated by recent experiments and density functional theory calculations on choloalite PbCuTe$_2$O$_6$, which possesses a Cu-based three-dimensional hyperkagome lattice, we propose and study a $J_1$-$J_2$-$J_3$ antiferromagnetic Heisenberg model on a hyperkagome lattice. In the classical limit, possible ground states are analyzed by two triangle rules, i.e., the "hyperkagome triangle rule" and the "isolated triangle rule," and classical Monte Carlo simulations are exploited to identify possible classical magnetic ordering and explore the phase diagram. In the quantum regime, Schwinger boson theory is applied to study possible quantum spin liquid states and long-range magnetically ordered states on an equal footing. These quantum states with bosonic partons are classified and analyzed by using projective symmetry groups (PSGs). It is found that there are only four types of algebraic PSGs allowed by the space group $P4_{1}32$ on a hyperkagome lattice. Moreover, there are only two types of PSGs that are compatible with the $J_1$-$J_2$-$J_3$ Heisenberg model. These two types of $Z_2$ bosonic states are distinguished by the gauge-invariant flux on the elementary ten-site loops on the hyperkagome network, called zero-flux state and $\pi$-flux state respectively. Both the zero-flux state and the $\pi$-flux state are able to give rise to quantum spin liquid states as well as magnetically ordered states, and the zero-flux states and the $\pi$-flux states can be distinguished by the lower and upper edges of the spectral function $S(\bm{q},\omega)$, which can be measured by inelastic neutron scattering experiments.
Evidence for free precession has been observed in the radio signature of several pulsars. Freely precessing pulsars radiate gravitationally at frequencies near the rotation rate and twice the rotation rate, which for rotation frequencies greater than $\sim 10$ Hz is in the LIGO band. In older work, the gravitational wave spectrum of a precessing neutron star has been evaluated to first order in a small precession angle. Here we calculate the contributions to second order in the wobble angle, and we find that a new spectral line emerges. We show that for reasonable wobble angles, the second-order line may well be observable with the proposed advanced LIGO detector for precessing neutron stars as far away as the galactic center. Observation of the full second-order spectrum permits a direct measurement of the star's wobble angle, oblateness, and deviation from axisymmetry, with the potential to significantly increase our understanding of neutron star structure.
We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by systematic errors. Our algorithm is designed to work with a general class of observables, such as low Fourier modes and local spatial averages over finite volume elements. Under suitable conditions on the relaxation (nudging) parameter, the spatial mesh resolution and the time step between successive measurements, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to a term which depends on the size of the errors. A stationary statistical analysis of our discrete data assimilation algorithm is also provided.
Space--time can be understood as some kind of space--time foam of fluctuating bubbles or loops which are expected to be an outcome of a theory of quantum gravity. One recently discussed model for this kind of space--time fluctuations is the holographic principle which allows to deduce the structure of these fluctuations. We review and discuss two scenarios which rely on the holographic principle leading to holographic noise. One scenario leads to fluctuations of the space--time metric affecting the dynamics of quantum systems: (i) an apparent violation of the equivalence principle, (ii) a modification of the spreading of wave packets, and (iii) a loss of quantum coherence. All these effects can be tested with cold atoms. These tests would supplement measurements of a so called ``mystery noise'' at the gravitational wave detector GEO600 which was recently speculated to have its origin in holographic noise.
It is shown that the long-term solar activity (represented by the dynamically covered monthly time series of the sunspot number for period 1750-2005yy) exhibits spectral properties of the Hamiltonian distributed chaos with spontaneously broken time translational symmetry.