ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $X$ be a smooth geometrically connected projective curve of genus two over a complete non-archimedean field $K$. For discretely valued $K$, the first main theorem in \cite{liu} gives a set of criteria on the Igusa invariants of the curve that determine the minimal Berkovich skeleton of $X$ together with its edge lengths and vertex weights. In this paper we use the theory of Berkovich spaces to give a new proof of this theorem that works for arbitrary complete non-archimedean fields. We furthermore interpret the final result in terms of tropical moduli spaces and tropical Igusa invariants. This reformulation shows that the abstract tropicalization map ${M}_{2}\to\mathrm{trop}(M_{2})$ factors through the tropicalization of a concrete embedding of ${M}_{2}$ into a weighted projective space.
A great effort is being made by the international Virtual Observatory community to build tools ready to be used by scientists. Presently, providing access to theoretical spectra in general, and synthetic spectra of galaxies in particular, is a matter of current interest in the Virtual Observatory. Several ways of accessing such spectra are available. We present two of them for accessing PEGASE.HR evolutionary synthesis models: HTTP-access to a limited number of parameters using Simple Spectral Access Protocol (SSAP), and full-featured WEB-service based access using Common Execution Architecture (CEA).
We show that spin-spin correlations in a non-Abelian Kitaev spin liquid are associated with a characteristic inhomogeneous charge density distribution in the vicinity of $\mathbb{Z}_2$ vortices. This density profile and the corresponding local electric fields are observable, e.g., by means of surface probe techniques. Conversely, by applying bias voltages to several probe tips, one can stabilize Ising anyons ($\mathbb{Z}_2$ vortices harboring a Majorana zero mode) at designated positions, where we predict a clear Majorana signature in energy absorption spectroscopy.
Feature tracking is a fundamental problem in computer vision, with applications in many computer vision tasks, such as visual SLAM and action recognition. This paper introduces a novel multi-body feature tracker that exploits a multi-body rigidity assumption to improve tracking robustness under a general perspective camera model. A conventional approach to addressing this problem would consist of alternating between solving two subtasks: motion segmentation and feature tracking under rigidity constraints for each segment. This approach, however, requires knowing the number of motions, as well as assigning points to motion groups, which is typically sensitive to the motion estimates. By contrast, here, we introduce a segmentation-free solution to multi-body feature tracking that bypasses the motion assignment step and reduces to solving a series of subproblems with closed-form solutions. Our experiments demonstrate the benefits of our approach in terms of tracking accuracy and robustness to noise.
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the singularities of solutions at the boundary. To this end, we derive mapping properties of Poisson operators in mixed scales with mixed smoothness. We also derive $\mathcal{R}$-sectoriality results for homogeneous boundary data in the case that the smoothness in normal direction is not too large.
We calculate explicitly an adelic quotient group for an excellent Noetherian normal integral two-dimensional separated scheme. An application to an irreducible normal projective algebraic surface over a field is given.
We propose a method for predicting the 3D shape of a deformable surface from a single view. By contrast with previous approaches, we do not need a pre-registered template of the surface, and our method is robust to the lack of texture and partial occlusions. At the core of our approach is a {\it geometry-aware} deep architecture that tackles the problem as usually done in analytic solutions: first perform 2D detection of the mesh and then estimate a 3D shape that is geometrically consistent with the image. We train this architecture in an end-to-end manner using a large dataset of synthetic renderings of shapes under different levels of deformation, material properties, textures and lighting conditions. We evaluate our approach on a test split of this dataset and available real benchmarks, consistently improving state-of-the-art solutions with a significantly lower computational time.
We examine, using mixed classical-quantum electron-ion dynamics, electron transfer in a donor-acceptor-like molecular junction system based on polyacetylene. We identify two qualitatively-different transfer regimes: hopping and tunnelling. We discuss the criteria for achieving each one and for minimizing inelastic scattering and decoherence arising from the coupling to the ions, and we connect our main results to quantities derived from electron dynamics involving simpler, three-state model systems. We identify the requirements to have near-ballistic transfer.
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when $\alpha=1$. For both problems, explicit solutions in terms of the Wright functions are presented. Even though the similarity of the two solutions, a proof that they are different is also given. The convergence when $\alpha \nearrow 1$ of the one and the other solutions to the same classical solution is given. Numerical examples for the dimensionless version of the problem are also presented and analyzed.
A novel crystal configuration of sandwiched S-Mo-Se structure (Janus SMoSe) at the monolayer limit has been synthesized and carefully characterized in this work. By controlled sulfurization of monolayer MoSe2 the top layer of selenium atoms are substituted by sulfur atoms while the bottom selenium layer remains intact. The peculiar structure of this new material is systematically investigated by Raman, photoluminescence and X-ray photoelectron spectroscopy and confirmed by transmission-electron microscopy and time-of-flight secondary ion mass spectrometry. Density-functional theory calculations are performed to better understand the Raman vibration modes and electronic structures of the Janus SMoSe monolayer, which are found to correlate well with corresponding experimental results. Finally, high basal plane hydrogen evolution reaction (HER) activity is discovered for the Janus monolayer and DFT calculation implies that the activity originates from the synergistic effect of the intrinsic defects and structural strain inherent in the Janus structure.
We study zeta-functions of weight lattices of compact connected semisimple Lie groups of type $A_3$. Actually we consider zeta-functions of SU(4), SO(6) and PU(4), and give some functional relations and new classes of evaluation formulas for them.
We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $\gamma$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.
Symmetry breaking perturbations in an electronically conducting medium are known to produce Friedel oscillations (FOs) in various physical quantities of an otherwise pristine material. Here we show in a mathematically transparent fashion that FOs in graphene have a strong sublattice asymmetry. As a result, the presence of impurities and/or defects may impact the distinct graphene sublattices very differently. Furthermore, such an asymmetry an be used to explain the recent observations that Nitrogen atoms and dimers are not randomly distributed in graphene but prefer to occupy one of its two distinct sublattices. We argue that this feature is not exclusive of Nitrogen and that it can be seen with other substitutional dopants.
Gribov theory is applied to investigate the shadowing effects in the structure functions of nuclei. In this approach these effects are related to the process of diffractive dissociation of a virtual photon. A model for this diffractive process, which describes well the HERA data, is used to calculate the shadowing in nuclear structure functions. A reasonable description of the $x$, $Q^2$ and A-dependence of nuclear shadowing is achieved.
The target tensor analyzing powers of the process $\gamma d -> \pi^{-}pp$ had been studied in the plane wave impulse approximation, if both ejected protons are detected in coincidence and in the directions, symmetrical respect to the incoming photon momentum, being in the proton plane. The matrix elements of the studied reaction become essentially simple, if the magnitudes of the proton momenta p1 = p2 = p are equal. That proton kinematics keeps the ejected pion angle near zero, therefore the one body pion production operator does not include the spin-non-flip term. Moreover, the transition to the triplet, spatially antisymmetric final pp- state is strongly suppressed from the symmetrical deuteron S - state as well as matrix elements have a large dependence from the orientation of the deuteron spin. The values of the $T_{22}(\vec p)$ component, calculated with three realistic deuteron wave functions in the proton momentum region p >= 350 MeV/c and proton polar angle theta >= 40 deg., differ one from another noticeably.
A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin-orbit splittings in neutron drops. This result is obtained from relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.
We investigate the possible development of magnetohydrodynamical instabilities in the EULAG-MHD "millenium simulation" of Passos & Charbonneau (2014). This simulation sustains a large-scale magnetic cycle characterized by solar-like polarity reversals taking place on a regular multidecadal cadence, and in which zonally-oriented bands of strong magnetic field accumulate below the convective layers, in response to turbulent pumping from above in successive magnetic half-cycles. Key aspects of this simulation include low numerical dissipation and a strongly subadiabatic fluid layer underlying the convectively unstable layers corresponding to the modeled solar convection zone. These properties are conducive to the growth and development of two-dimensional instabilities otherwise suppressed by stronger dissipation. We find evidence for the action of a non-axisymmetric magnetoshear instability operating in the upper portions of the stably stratified fluid layers. We also investigate the possibility that the Tayler instability may be contributing to the destabilization of the large-scale axisymmetric magnetic component at high latitudes. On the basis of our analyses, we propose a global dynamo scenario whereby the magnetic cycle is driven primarily by turbulent dynamo action in the convecting layers, but MHD instabilities accelerate the dissipation of the magnetic field pumped down into the overshoot and stable layers, thus perhaps significantly influencing the magnetic cycle period. Support for this scenario is found in the distinct global dynamo behaviors observed in an otherwise identical EULAG-MHD simulations, using a different degree of subadiabaticity in the stable fluid layers underlying the convection zone.
Using the framework for solving the spherically symmetric field equations in observational coordinates given in Araujo and Stoeger (1999), their formulation and solution in the perturbed FLRW sperically symmetric case with observational data representing galaxy redshifts, number counts and observer area distances, both as functions of redshift on our past light cone, are presented. The importance of the central conditions, those which must hold on our world line C, is emphasized. In detailing the solution for these perturbations, we discuss the gauge problem and its resolution in this context, as well as how errors and gaps in the data are propagated together with the genuine perturbations. This will provide guidance for solving, and interpreting the solutions of the more complicated general perturbation problem with observational data on our past light cone.
The electron energy spectra, not connected to b-decay, of 235U- and 239Pu-films, irradiated by thermal neutrons, obtained by a Monte Carlo method is presented in the given work. The modelling was performed with the help of a computer code MCNP4C (Monte Carlo Neutron Photon transport code system), allowing to carry out the computer experiments on joint transport of neutrons, photons and electrons. The experiment geometry and the parameters of an irradiation were the same, as in [11] (the thickness of a foil varied only). As a result of computer experiments, the electron spectra was obtained for the samples of 235U, 239Pu and uranium dioxide of 93 % enrichment representing a set of films of 22 mm in diameter and different thickness: 0,001 mm, 0,005 mm, 0,02 mm, 0,01 mm, 0,1 mm, 1,0 mm; and also for the uranium dioxide film of 93 % enrichment (diameter 22 mm and thickness 0,01mm), located between two protective 0,025 mm aluminium disks (the conditions of experiment in [11]) and the electron spectrum was fixed at the output surface of a protective disk. The comparative analysis of the experimental [11] and calculated b--spectra is carried out.
We propose a novel scheme to implement a quantum controlled phase gate for trapped ions in thermal motion with one standing wave laser pulse. Instead of applying the rotating wave approximation this scheme makes use of the counter-rotating terms of operators. We also demonstrate that the same scheme can be used to generate maximally entangled states of $N$ trapped ions by a single laser pulse.
We calculate the shadowing of sea quarks and gluons and show that the shadowing of gluons is {\it not} simply given by the sea quark shadowing, especially at small $x$. The calculations are done in the lab frame approach by using the generalized vector meson dominance model. Here the virtual photon turns into a hadronic fluctuation long before the nucleus. The subsequent coherent interaction with more than one nucleon in the nucleus leads to the depletion $\sigma (\gamma^* A) < A\sigma (\gamma^* N)$ known as shadowing. A comparison of the shadowing of quarks to E665 data for $^{40}Ca$ and $^{207}Pb$ shows good agreement.
Flat bands are of extreme interest in a broad spectrum of fields since given by their high degeneracy, a small perturbation introduced in the system is able to push the ground state in the direction of an ordered phase of interest. Hence the flat band engineering in real materials attracts huge attention. However, manufacturing a flat band represents a difficult task because its appearance in a real system is connected to rigid mathematical conditions relating a part of Hamiltonian parameters. Consequently, whenever a flat band is desired to be manufactured, these Hamiltonian parameters must be tuned exactly to the values fixed by these rigid mathematical conditions. Here we demonstrate that taking the many-body spin-orbit interaction (SOI) into account -- which can be continuously tuned e.g. by external electric fields --, these rigid mathematical conditions can be substantially relaxed. On this line we show that a $\sim 20-30 \%$ variation in the Hamiltonian parameters rigidly fixed by the flat band conditions can also lead to flat bands in the same or in a bit displaced position on the energy axis. This percentage can even increase to $\sim 80 \%$ in the presence of an external magnetic field. The study is made in the case of conducting polymers. These systems are relevant not only because they have broad application possibilities, but also because they can be used to present the mathematical background of the flat band conditions in full generality, in a concise, clear and understandable manner applicable everywhere in itinerant systems.
A comprehensive description of the optical cycle of spin defects in solids requires the understanding of the electronic and atomistic structure of states with different spin multiplicity, including singlet states which are particularly challenging from a theoretical standpoint. We present a general framework, based on spin-flip time-dependent density function theory, to determine the excited state potential energy surfaces of the many-body singlet states of spin defects; we then predict the vibrationally resolved absorption spectrum between singlet shelving states of a prototypical defect, the nitrogen-vacancy center in diamond. Our results, which are in excellent agreement with experiments, provide an interpretation of the measured spectra and reveal the key role of specific phonons in determining absorption processes, and the notable influence of non-adiabatic interactions. The insights gained from our calculations may be useful in defining strategies to improve infrared-absorption-based magnetometry and optical pumping schemes. The theoretical framework developed here is general and applicable to a variety of other spin defects and materials.
We calculate the partition functions of QCD in two dimensions on a cylinder and on a torus in the gauge $\partial_{0} A_{0} = 0$ by integrating explicitly over the non zero modes of the Fourier expansion in the periodic time variable. The result is a one dimensional Kazakov-Migdal matrix model with eigenvalues on a circle rather than on a line. We prove that our result coincides with the standard expansion in representations of the gauge group. This involves a non trivial modular transformation from an expansion in exponentials of $g^2$ to one in exponentials of $1/g^2$. Finally we argue that the states of the $U(N)$ or $SU(N)$ partition function can be interpreted as a gas of N free fermions, and the grand canonical partition function of such ensemble is given explicitly as an infinite product.
Understanding thermal transport in nanoscale systems presents important challenges to both theory and experiment. In particular, the concept of local temperature at the nanoscale appears difficult to justify. Here, we propose a novel theoretical approach where we replace the temperature gradient with controllable external black-body radiations. The theory recovers known physical results, for example the linear relation between the thermal current and the temperatures difference of two black-bodies. Furthermore, our theory is not limited to the linear regime and goes beyond accounting for non linear effects and transient phenomena. In the strong coupling and large temperature gradients, we show that there is a maximum energy current that the system can sustain and we recover the Kramers' turnover. Since the present theory is general and can be adapted to describe both electron and phonon dynamics, it provides a first step towards a unified formalism for investigating thermal and electronic transport.
Minimal irregular surfaces of general type satisfy K^2\geq 2p_g. In this paper we classify those surfaces for which the equality K^2=2p_g holds.
We present Herschel far-IR photometry and spectroscopy as well as ground based CO observations of an intermediate redshift (0.21 < z < 0.88) sample of Herschel-selected (ultra)-luminous infrared galaxies (L_IR > 10^11.5L_sun). With these measurements we trace the dust continuum, far-IR atomic line emission, in particular [CII]\,157.7microns, as well as the molecular gas of z~0.3 (U)LIRGs and perform a detailed investigation of the interstellar medium of the population. We find that the majority of Herschel-selected intermediate redshift (U)LIRGs have L_CII/L_FIR ratios that are a factor of about 10 higher than that of local ULIRGs and comparable to that of local normal and high-$z$ star forming galaxies. Using our sample to bridge local and high-z [CII] observations, we find that the majority of galaxies at all redshifts and all luminosities follow a L_CII-L_FIR relation with a slope of unity, from which local ULIRGs and high-z AGN dominated sources are clear outliers. We also confirm that the strong anti-correlation between the L_CII/L_FIR ratio and the far-IR color L_60/L_100 observed in the local Universe holds over a broad range of redshifts and luminosities, in the sense that warmer sources exhibit lower L_CII/L_FIR at any epoch. Intermediate redshift ULIRGs are also characterised by large molecular gas reservoirs and by lower star formation efficiencies compared to that of local ULIRGs. The high L_CII/L_FIR ratios, the moderate star formation efficiencies (L_LIR/L_CO or L_IR/M_gas) and the relatively low dust temperatures of our sample (which are also common characteristics of high-z star forming galaxies with ULIRG-like luminosities) indicate that the evolution of the physical properties of (U)LIRGs between the present day and z > 1 is already significant by z ~ 0.3.
R-parity violating bilinear (soft) terms in the supersymmetric standard model would be the leading source for nonzero neutrino masses and mixing. We point out that the mixing between neutralinos (charginos) and neutrinos (charged leptons) driven by the bilinear terms take factorized forms, which may enable us to probe the neutrino mixing parameters in a collider. It is then shown that the Super-Kamiokande data on atmospheric neutrinos require all the baryon number violating couplings to be substantially suppressed: $\lambda''_{\rm any} <10^{-9}$.
Gamow-Teller (GT) transitions play an important and consequential role in many astrophysical phenomena. These include, but are not limited to, electron and positron capture rates which determine the fate of massive stars and play an intricate role in the dynamics of core collapse. These $GT_{\pm}$ transitions rates are the significant inputs in the description of supernova explosions. $GT_{\pm}$ strength function values are sensitive to the $^{56}Ni$ core excitation in the middle \textit{pf}-shell region and to the size of the model space as well. We used the pn-QRPA theory for extracting the GT strength for ground and excited states of $^{56}Ni$. We then used these GT strength distributions to calculate the electron \textit{and} positron capture rates which show differences with the earlier calculations. One curious finding of this paper is our enhanced electron capture rates on $^{56}Ni$ at presupernova temperatures. These differences need to be taken into account for the modeling of the early stages of Type II supernova evolution.
A model of a spin valve in which electron transport between the magnetized electrodes is due to multistep tunneling is analyzed. Motivated by recent experiments on organic spin valves, we assume that spin memory loss in the course of transport is due to random hyperfine fields acting on electron while it waits for the next tunneling step. Amazingly, we identify the three-step configurations of sites, for which the tunnel magnetoresistance (TMR) is negative, suggesting that the resistance for antiparallel magnetizations of the electrodes is smaller than for parallel magnetizations. We analyze the phase volume of these configurations with respect to magnitudes and relative orientations of the on-site hyperfine fields. The effect of sign reversal of TMR is exclusively due to interference of the spin-flip amplitudes on each site, it does not emerge within commonly accepted probabilistic description of spin transport. Another feature specific to multistep inelastic tunneling is bouncing of electron between nearest neighbors while awaiting a "hard" hop. We demonstrate that this bouncing, being absolutely insignificant for conduction of current, can strongly affect the spin memory loss. This effect is also of interference origin.