ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study one-loop effects of sfermions on helicity amplitudes for $\eeww$ in the Minimal Supersymmetric Standard Model. The one-loop contributions are calculated in the $\bar{\rm MS}$ renormalization scheme. In order to verify the validity of the analytic calculation and the numerical program, the following tests are performed. (i) The BRS sum rules hold exactly among the analytic expressions of the form factors of the $\eeww$ amplitude and those of the amplitudes where the external $W^\pm$ bosons are replaced by the corresponding Goldstone bosons $\chi^\pm$, hence they hold within the expected accuracy of the numerical program. (ii) The one-loop sfermion contribution to the amplitudes decouple in the heavy mass limit. This property is used to test the overall normalization of the amplitudes. In order to observe the analytically exact decoupling, the amplitudes are expanded by the $\bar{\rm MS}$ couplings of the Standard Model. (iii) The high-energy analytic formulas of the helicity amplitudes, which are verified by using the equivalence theorem analytically, are used for the numerical test of the high energy behavior of the amplitudes. We then investigate the magnitude of the one-loop effects on each helicity amplitude which may be measured by experiments at future linear colliders. Under the constraint from available precision data, the one-loop corrections to a few helicity amplitudes (for example, the longitudinal-$W$-pair production) can be at most from -0.8% to $+0.6$% in magnitude in the observables. The corrections in the helicity-summed cross sections are smaller, typically a few times $\pm 0.1$% at large scattering angles.
In this paper we investigate the following fractional order in time Cauchy problem \begin{equation*} \begin{cases} \mathbb{D}_{t}^{\alpha }u(t)+Au(t)=f(u(t)), & 1<\alpha <2, u(0)=u_{0},\,\,\,u^{\prime }(0)=u_{1}. & \end{cases}% \end{equation*}% The fractional in time derivative is taken in the classical Caputo sense. In the scientific literature such equations are sometimes dubbed as fractional-in time wave equations or super-diffusive equations. We obtain results on existence and regularity of local and global weak solutions assuming that $A$ is a nonnegative self-adjoint operator with compact resolvent in a Hilbert space and with a nonlinearity $f\in C^{1}({\mathbb{R}}% )$ that satisfies suitable growth conditions. Further theorems on the existence of strong solutions are also given in this general context.
We present a model to calculate cross sections for electroinduced two-nucleon emission from finite nuclei. Short-range correlations in the wave functions and meson-exchange contributions to the photoabsorption process are implemented. Effects of the short-range correlations are studied with the aid of a perturbation expansion method with various choices of the Jastrow correlation function. The model is used to investigate the relative importance of the different reaction mechanisms contributing to the A(e,e$'$pn) and A(e,e$'$pp) process. Representative examples for the target nuclei $^{12}$C and $^{16}$O and for kinematical conditions accessible with contemporary high-duty cycle electron accelerators are presented. A procedure is outlined to calculate the two-nucleon knockout contribution to the semi-exclusive (e,e$'$p) cross section. Using this technique we investigate in how far semi-exclusive (e,e$'$p) reactions can be used to detect high-momentum components in the nuclear spectral function.
We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.
Topological band insulators which are dynamically generated by electron-electron interactions have been the- oretically proposed in two and three dimensional lattice models. We present evidence that the two-dimensional version can be stabilized in digital (111) heterostructures of transition-metal oxides as a result of purely local interactions. The topological phases are accompanied by spontaneous ordering of complex orbitals and we discuss their stability with respect to the Hund's rule coupling, Jahn-Teller interaction and inversion symmetry breaking terms. As main competitors we identify spin-nematic and magnetic phases.
We prove formulae for the motives of stacks of coherent sheaves of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with rational coefficients.
Calculus of Variation combined with Differential Geometry as tools of modelling and solving problems in image processing and computer vision were introduced in the late 80's and the 90s of the 20th century. The beginning of an extensive work in these directions was marked by works such as Geodesic Active Contours (GAC), the Beltrami framework, level set method of Osher and Sethian the works of Charpiat et al. and the works by Chan and Vese to name just a few. In many cases the optimization of these functional are done by the gradient descent method via the calculation of the Euler-Lagrange equations. Straightforward use of the resulted EL equations in the gradient descent scheme leads to non-geometric and in some cases non sensical equations. It is costumary to modify these EL equations or even the functional itself in order to obtain geometric and/or sensical equations. The aim of this note is to point to the correct way to derive the EL and the gradient descent equations such that the resulted gradient descent equation is geometric and makes sense.
All-solid-state lithium batteries promise significant improvements in energy density and safety over traditional liquid electrolyte batteries. The Al-doped AlxLi7-3xLa3Zr2O12 (LLZO) solid-state electrolyte shows excellent potential given its high ionic conductivity and good thermal, chemical, and electrochemical stability. Nevertheless, further improvements on LLZOs electrochemical and mechanical properties call for an incisive understanding of its local microstructure. Here, we employ Bragg Coherent Diffractive Imaging to investigate the atomic displacements inside single grains of LLZO with various Al-doping concentrations, resulting in cubic, tetragonal, and cubic-tetragonal mixed structures. We observe coexisting domains of different crystallographic orientations in the tetragonal structure. We further show that Al doping leads to crystal defects such as dislocations and phase boundary in the mixed- and cubic-phase grain. This study addresses the effect of Al-doping on the nanoscale structure within individual grains of LLZO, which is informative for the future development of solid-state batteries.
We characterize the subexponential densities on $(0,\infty)$ for compound Poisson distributions on $[0,\infty)$ with absolutely continuous L\'evy measures. As a corollary, we show that the class of all subexponential probability density functions on $\mathbb R_+$ is closed under generalized convolution roots of compound Poisson sums. Moreover, we give an application to the subexponential density on $(0,\infty)$ for the distribution of the supremum of a random walk.
Spin-pumping across ferromagnet/superconductor (F/S) interfaces has attracted much attention lately. Yet the focus has been mainly on s-wave superconductors-based systems whereas (high-temperature) d-wave superconductors such as YBa2Cu3O7-d (YBCO) have received scarce attention despite their fundamental and technological interest. Here we use wideband ferromagnetic resonance to study spin-pumping effects in bilayers that combine a soft metallic Ni80Fe20 (Py) ferromagnet and YBCO. We evaluate the spin conductance in YBCO by analyzing the magnetization dynamics in Py. We find that the Gilbert damping exhibits a drastic drop as the heterostructures are cooled across the normal-superconducting transition and then, depending on the S/F interface morphology, either stays constant or shows a strong upturn. This unique behavior is explained considering quasiparticle density of states at the YBCO surface, and is a direct consequence of zero-gap nodes for particular directions in the momentum space. Besides showing the fingerprint of d-wave superconductivity in spin-pumping, our results demonstrate the potential of high-temperature superconductors for fine tuning of the magnetization dynamics in ferromagnets using k-space degrees of freedom of d-wave/F interfaces.
Simpson, in 1994, introduced the notion of $\Lambda$-modules and constructed the corresponding moduli space, where $\Lambda$ is a sheaf of rings of differential operators. Higgs bundles, connections and $\lambda$-connections (as defined by Delgine) are particular cases of $\Lambda$-modules. In this article the concept of parabolic $\Lambda$-modules over a curve is introduced and their moduli space is built. As an application, we construct the parabolic Hodge moduli space parameterizing parabolic $\lambda$-connections.
In this survey paper we review recent advances in the calculus of Chern-Schwartz-MacPherson, motivic Chern, and elliptic classes of classical Schubert varieties. These three theories are one-parameter ($\hbar$) deformations of the notion of fundamental class in their respective extraordinary cohomology theories. Examining these three classes in conjunction is justified by their relation to Okounkov's stable envelope notion. We review formulas for the $\hbar$-deformed classes originating from Tarasov-Varchenko weight functions, as well as their orthogonality relations. As a consequence, explicit formulas are obtained for the Littlewood-Richardson type structure constants.
We report on the depth dependence and technological limits of the phase transition of the iron rhodium alloy as function of temperature, external magnetic and electric fields in the FeRh/BaTiO3 multiferroic, determined by grazing-incidence nuclear resonant scattering measurements. The change of temperature induces a continuous and homogenous antiferromagnetic / ferromagnetic phase transition through the entire FeRh layer, except in the near substrate region. External magnetic field does not affect this mechanism, but the application of electric field changes it fundamentally (via piezoelectric strain): the phase transition of the alloy suddenly propagates from the substrate up to a height, defined by the combination of temperature and external magnetic field, as soon as the applied electric field reaches ~ 20 kV/m.
We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier-Stokes equations supplemented with H^1 initial velocity and only bounded nonnegative density. In contrast with all the previous works on that topics, we do not require regularity or positive lower bound for the initial density, or compatibility conditions for the initial velocity, and still obtain unique solutions. Those solutions are global in the two-dimensional case for general data, and in the three-dimensional case if the velocity satisfies a suitable scaling invariant smallness condition. As a straightforward application, we provide a complete answer to Lions' question in [25], page 34, concerning the evolution of a drop of incompressible viscous fluid in the vacuum.
Simulations support the conjecture that the dimension of the trace of Brownian earthworm is strictly greater than 3/2.
We present a comprehensive analysis of 21 light curves of Type 1 AGN from the Kepler spacecraft. First, we describe the necessity and development of a customized pipeline for treating Kepler data of stochastically variable sources like AGN. We then present the light curves, power spectral density functions (PSDs), and flux histograms. The light curves display an astonishing variety of behaviors, many of which would not be detected in ground-based studies, including switching between distinct flux levels. Six objects exhibit PSD flattening at characteristic timescales which roughly correlate with black hole mass. These timescales are consistent with orbital timescales or freefall accretion timescales. We check for correlations of variability and high-frequency PSD slope with accretion rate, black hole mass, redshift and luminosity. We find that bolometric luminosity is anticorrelated with both variability and steepness of the PSD slope. We do not find evidence of the linear rms-flux relationships or lognormal flux distributions found in X-ray AGN light curves, indicating that reprocessing is not a significant contributor to optical variability at the 0.1-10% level.
The Milky Way's center is the closest galaxy nucleus and the most extreme environment of the Galaxy. Although its volume is less than 1% of that of the Galactic disk, up to 10% of all new-born stars in the Galaxy in the past 100 Myr formed there. Therefore, it constitutes a perfect laboratory to understand star formation under extreme conditions, similar to those in starburst or high-redshift galaxies. However, the only two known Galactic center young clusters account for <10% of the expected young stellar mass. We analyze the star formation history of Sagittarius (Sgr) B1, a Galactic center region associated with strong HII emission, and find evidence for the presence of several $10^5$ solar masses of young stars, that formed $\sim$10 Myr ago. We also detect the presence of intermediate age stars (2-7 Gyr) in Sgr B1 that appear to be rare (or absent) in the inner regions of the nuclear stellar disk, and might indicate inside out formation. Our results constitute a large step toward a better understanding of star formation at the Galactic center, such as the fate of young clusters, and the possibly different initial mass function in this region.
A temperature-dependent EXAFS investigation of La{1-x}Ca{x}MnO3 is presented for the concentration range that spans the ferromagnetic-insulator (FMI) to ferromagnetic-metal (FMM) transition region, x = 0.16-0.22. The samples are insulating for x = 0.16-0.2 and show a metal/insulator transition for x = 0.22. All samples are ferromagnetic although the saturation magnetization for the 16% Ca sample is only ~ 70% of the expected value at 0.4T. We find that the FMI samples have similar correlations between changes in the local Mn-O distortions and the magnetization as observed previously for the colossal magnetoresistance (CMR) samples (0.2 < x < 0.5) - except that the FMI samples never become fully magnetized. The data show that there are at least two distinct types of distortions. The initial distortions removed as the insulating sample becomes magnetized are small and provides direct evidence that roughly 50% of the Mn sites have a small distortion/site and are magnetized first. The large remaining Mn-O distortions at low T are attributed to a small fraction of Jahn-Teller-distorted Mn sites that are either antiferromagnetically ordered or unmagnetized. Thus the insulating samples are very similar to the behavior of the CMR samples up to the point at which the M/I transition occurs for the CMR materials. The lack of metallic conductivity for x <= 0.2, when 50% or more of the sample is magnetic, implies that there must be preferred magnetized Mn sites and that such sites do not percolate at these concentrations.
Observed reddening in the circum-galactic medium (CGM) indicates a significant abundance of small grains, of which the origin is still to be clarified. We examine a possible path of small-grain production through shattering of pre-existing large grains in the CGM. Possible sites where shattering occurs on a reasonable time-scale are cool clumps with hydrogen number density $n_\mathrm{H}\sim 0.1$ cm$^{-3}$ and gas temperature $T_\mathrm{gas}\sim 10^4$ K, which are shown to exist through observations of Mg II absorbers. We calculate the evolution of grain size distribution in physical conditions appropriate for cool clumps in the CGM, starting from a large-grain-dominated distribution suggested from theoretical studies. With an appropriate gas turbulence model expected from the physical condition of cold clumps (maximum eddy size and velocity of $\sim$100 pc and 10 km s$^{-1}$, respectively), together with the above gas density and temperature and the dust-to-gas mass ratio inferred from observations (0.006), we find that small-grain production occurs on a time-scale (a few $\times 10^8$ yr) comparable to the lifetime of cool clumps derived in the literature. Thus, the physical conditions of the cool clouds are favrourable for small-grain production. We also confirm that the reddening becomes significant on the above time-scale. Therefore, we conclude that small-grain production by shattering is a probable cause for the observed reddening in the CGM. We also mention the effect of grain materials (or their mixtures) on the reddening at different redshifts (1 and 2).
We study the diagonalizability of the Atkin $U$-operator acting on Drinfeld cusp forms for $\Gamma_1(t)$ and $\Gamma(t)$ using Teitelbaum's interpretation as harmonic cocycles. We prove $U$ is diagonalizable for small weights and explicitly compute the eigenvalues. We also formulate a conjecture, supported by numerical search and proofs in some special cases, about non diagonalizability of $U$ in even characteristic.
In this paper, we study a scalar linearly growing BSDE with a weakly $L^{1+}$-integrable terminal value. We prove that the BSDE admits a solutionif the terminal value satisfies some $\Psi$-integrability condition, which is weaker than the usual $L^p$ ($p>1$) integrability and stronger than $L\log L$ integrability. We show by a counterexample that $L\log L$ integrability is not sufficient for the existence of solutionto a BSDE of a linearly growing generator.
By analysing the work of Campolattaro we argue that the second Seiberg-Witten equation over the Spin^c_4 manifold, i.e., F^+_{ij}=< M,S_ij M >, is the generalization of the Campolattaro's description of the electromagnetic field tensor F^{\mu\nu} in the bilinear form F^{\mu\nu}=\bar{\Psi} S^{\mu\nu}\Psi. It turns out that the Seiberg-Witten equations (also the perturbed Seiberg-Witten equations) can be well understood from this point of view. We suggest that the second Seiberg-Witten equation can be replaced by a nonlinear Dirac-like Equation. We also derive the spinor representation of the connection on the associated unitary line bundle over the Spin^c_4 manifold.
We find that the exponential operator V=exp[ilamda (Q_1P_2+Q_2P_3+...+Q_{n-1}P_{n}+Q_{n}P_1)], Q_{i}, P_{i} are respectively the coordinate and momentum operators, is an n-mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V's normally ordered expansion and obtain the n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.
To improve the performance of blind face restoration, recent works mainly treat the two aspects, i.e., generic and specific restoration, separately. In particular, generic restoration attempts to restore the results through general facial structure prior, while on the one hand, cannot generalize to real-world degraded observations due to the limited capability of direct CNNs' mappings in learning blind restoration, and on the other hand, fails to exploit the identity-specific details. On the contrary, specific restoration aims to incorporate the identity features from the reference of the same identity, in which the requirement of proper reference severely limits the application scenarios. Generally, it is a challenging and intractable task to improve the photo-realistic performance of blind restoration and adaptively handle the generic and specific restoration scenarios with a single unified model. Instead of implicitly learning the mapping from a low-quality image to its high-quality counterpart, this paper suggests a DMDNet by explicitly memorizing the generic and specific features through dual dictionaries. First, the generic dictionary learns the general facial priors from high-quality images of any identity, while the specific dictionary stores the identity-belonging features for each person individually. Second, to handle the degraded input with or without specific reference, dictionary transform module is suggested to read the relevant details from the dual dictionaries which are subsequently fused into the input features. Finally, multi-scale dictionaries are leveraged to benefit the coarse-to-fine restoration. Moreover, a new high-quality dataset, termed CelebRef-HQ, is constructed to promote the exploration of specific face restoration in the high-resolution space.
We prove tight estimates for averages of the twisted Hooley $\Delta$-function over arbitrary number fields.
We present far-IR photometry and infrared spectrum of the z=3.9114 quasar/starburst composite system APM 08279+5255 obtained using the Stratospheric Observatory for Infrared Astronomy (SOFIA)/HAWC+ and the Spitzer Space Telescope Infrared Spectrograph (IRS). We decompose the IR-to-radio spectral energy distribution (SED), sampled in 51 bands, using (i) a model comprised of two-temperature modified blackbodies (MBB) and radio power-laws and (ii) a semi-analytic model, which also accounts for emission from a clumpy torus. The latter is more realistic but requires a well-sampled SED, as possible here. In the former model, we find temperatures of T_warm = 296^17_15 K and T_cold = 110^3_3 K for the warm and cold dust components, respectively. This model suggests that the cold dust component dominates the FIR energy budget (66%) but contributes only 17% to the total IR luminosity. Based on the torus models, we infer an inclination angle of i=15^8_8 degree and the presence of silicate emission, in accordance with the Type-1 active galactic nucleus nature of APM 08279+5255. Accounting for the torus' contribution to the FIR luminosity, we find a lensing-corrected star formation rate of SFR=3075x(4/mu_L) Msun yr^-1. We find that the central quasar contributes 30% to the FIR luminosity but dominates the total IR luminosity (93%). The 30% correction is in contrast to the 90% reported in previous work. In addition, the IR luminosity inferred from the torus model is a factor of two higher. These differences highlight the importance of adopting physically motivated models to properly account for IR emission in high-z quasars, which is now possible with SOFIA/HAWC+.
When using black hole excision to numerically evolve a fully generic black hole spacetime, most 3-D 3+1 codes use an $xyz$-topology (spatial) grid. In such a grid, an $r = \constant$ excision surface must be approximated by an irregular and non-smooth "staircase-shaped" excision grid boundary, which may introduce numerical instabilities into the evolution. In this paper I describe an alternate scheme, which uses multiple grid patches, each with topology $\{r \times ({\rm angular coordinates})\}$, to cover the slice outside the $r = \constant$ excision surface. The excision grid boundary is now smooth, so the evolution should be less prone to instabilities. With 4th order finite differencing, this code evolves Kerr initial data to ${\sim} 60M$ using the ADM equations; I'm currently implementing the BSSN equations in it in the hope that this will improve the stability.
The properties of the ground state of $^{178}$Hf and the isomeric state $^{178}$Hf$^{m2}$ are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of $^{178}$Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with $K^\pi=16^+$ is found to be $\nu(7/2^-[514])^{-1}(9/2^+[624])^{1}$ $\pi(7/2^+[404])^{-1}(9/2^-[514])^{1}$. Its excitation energy calculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the $^{178}$Hf$^{m2}$ experimental excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.