ShantanuT01/DACTYL-Pretraining huggingface dataset:
While Kerr effect has been used extensively for the study of magnetic materials, it is only recently that its has shown to be a powerful tool for the study of more complex quantum matter. Since such materials tend to exhibit a wealth of new phases and broken symmetries, it is important to understand the general constraints on the possibility of observing a finite Kerr effect. In this paper we reviewed the consequences of reciprocity on the scattering of electromagnetic waves. In particular we concentrate on the possible detection of Kerr effect from chiral media with and without time-reversal symmetry breaking. We show that a finite Kerr effect is possible only if reciprocity is broken. Introducing the utilization of the Sagnac interferometer as a detector for breakdown of reciprocity via the detection of a finite Kerr effect, we argue that in the linear regime, a finite detection is possible only if reciprocity is broken. We then discuss possible Kerr effect detection for materials with natural optical activity, magnetism, and chiral superconductivity.
In this article, we study the geometry of plane curves obtained by three sections and another section given as their sum on certain rational elliptic surfaces. We make use of Mumford representations of semi-reduced divisors in order to study the geometry of sections. As a result, we are able to give new proofs for some classical results on singular plane quartics and their bitangent lines.
A novel scene text recognizer based on Vision-Language Transformer (VLT) is presented. Inspired by Levenshtein Transformer in the area of NLP, the proposed method (named Levenshtein OCR, and LevOCR for short) explores an alternative way for automatically transcribing textual content from cropped natural images. Specifically, we cast the problem of scene text recognition as an iterative sequence refinement process. The initial prediction sequence produced by a pure vision model is encoded and fed into a cross-modal transformer to interact and fuse with the visual features, to progressively approximate the ground truth. The refinement process is accomplished via two basic character-level operations: deletion and insertion, which are learned with imitation learning and allow for parallel decoding, dynamic length change and good interpretability. The quantitative experiments clearly demonstrate that LevOCR achieves state-of-the-art performances on standard benchmarks and the qualitative analyses verify the effectiveness and advantage of the proposed LevOCR algorithm. Code is available at https://github.com/AlibabaResearch/AdvancedLiterateMachinery/tree/main/OCR/LevOCR.
We present light curves and periods of 53 candidates for short period eclipsing binary stars identified by SuperWASP. These include 48 newly identified objects with periods <2x10^4 seconds (~0.23d), as well as the shortest period binary known with main sequence components (GSC2314-0530 = 1SWASP J022050.85+332047.6) and four other previously known W UMa stars (although the previously reported periods for two of these four are shown to be incorrect). The period distribution of main sequence contact binaries shows a sharp cut-off at a lower limit of around 0.22d, but until now, very few systems were known close to this limit. These new candidates will therefore be important for understanding the evolution of low mass stars and to allow investigation of the cause of the period cut-off.
Let $\rho$ be a mod $\ell$ Galois representation. We show how to compute $\rho$, given the characteristic polynomial of the image of the Frobenius at one prime $p$ and a curve $C$ whose Jacobian contains $\rho$ in its $\ell$-torsion. The main ingredient is a method to $p$-adically lift torsion points on a Jacobian in the framework of Makdisi's algorithms.
We extend the recent Solymosi's sum-product estimate for reals to the complex case.
In this paper we prove the existence of phase transitions at finite temperature for O(n) classical ferromagnetic spin models on infrared finite graphs. Infrared finite graphs are infinite graphs with $\lim {m\to 0^+} {\bar Tr (L+m)^{-1} < \infty$, where $L$ is the Laplacian operator of the graph. The ferromagnetic couplings are only requested to be bounded by two positive constants. The proof, inspired by the classical result of Fr\"ohlich, Simon and Spencer on lattices, is given through a rigorous bound on the average magnetization. The result holds for $n\ge 1$ and it includes as a particular case the Ising model.
Given a simple connected graph on $N$ vertices with size $|E|$ and degree sequence $d_{1}\leq d_{2}\leq ...\leq d_{N}$, the aim of this paper is to exhibit new upper and lower bounds for the additive degree-Kirchhoff index in closed forms, not containing effective resistances but a few invariants $(N,|E|$ and the degrees $d_{i}$) and applicable in general contexts. In our arguments we follow a dual approach: along with a traditional toolbox of inequalities we also use a relatively newer method in Mathematical Chemistry, based on the majorization and Schur-convex functions. Some theoretical and numerical examples are provided, comparing the bounds obtained here and those previously known in the literature.
We have observed asymmetric Fano resonances in the conductance of a single electron transistor resulting from interference between a resonant and a nonresonant path through the system. The resonant component shows all the features typical of quantum dots, but the origin of the non-resonant path is unclear. A unique feature of this experimental system, compared to others that show Fano line shapes, is that changing the voltages on various gates allows one to alter the interference between the two paths.
We study a ferromagnetic Heisenberg spin system on the square lattice, with nearest neighbors interaction J_1 frustrated by second J_2 and third J_3 neighbors antiferromagnetic interactions, using a mean field theory for the Schwinger boson representation of spins. For J_3=0 we find that the boundary between the ferromagnetic and the collinear classical phases shifts to smaller values of J_2 when quantum fluctuations are included. Along the line J_2/|J_1|= 1 the boundaries between the collinear and incommensurate regions are strongly shifted to larger values with respect to the classical case. We do not find clear evidence for spin gapped phases within the present approximation.
In this paper, we prove that the solution maps of a large class of nonlocal dispersal equations are $\alpha$-contractions, where $\alpha$ is the Kuratowski measure of noncompactness. Then we give some remarks on the spreading speeds and traveling waves for such evolution equations in a periodic habitat.
Cosmological hydrodynamical simulations predict that a large fraction of all baryons reside within mildly non-linear structures with temperatures in the range $10^{5}-10^{7}$K. As the gas is highly ionized, it could be detected by the temperature anisotropies generated on the Cosmic Microwave Background radiation. We refine our previous estimates of the thermal Sunyaev-Zeldovich effect by introducing a non-polytropic equation of state to model the temperature distribution of the shock heated gas derived from temperature-density phase diagrams of different hydrodynamical simulations. Depending on the specific model, the Comptonization parameter varies in the range $10^{-7}\le y_c \le 2\times 10^{-6}$, compatible with the FIRAS upper limit. This amplitude is in agreement with a simple toy model constructed to estimate the average effect induced by filaments of ionized gas. Using the log-normal probability density function we calculate the correlation function and the power spectrum of the temperature anisotropies generated by the WHIM filaments. For a wide range of the parameter space, the maximum amplitude of the radiation power spectrum is $(\ell+1)\ell C_{\ell}/2\pi =0.7-70(\mu K)^2$ at $\ell \approx 200-500$. This amplitude scales with baryon density, Hubble constant and the amplitude of the matter power spectrum $\sigma_8$ as $[(\ell+1)\ell C_\ell]_{\mathrm{max}}/2\pi \propto \sigma_8^{2.6}(\Omega_b h)^2$. Since the thermal Sunyaev-Zeldovich effect has a specific frequency dependence, we analyze the possibility of detecting this component with the forthcoming Planck data.
The present paper focuses on the high-mass star-forming region G23.01-0.41. Methods: Using the VLBA and the EVN arrays, we conducted phase-referenced observations of the three most powerful maser species in G23.01-0.41: H2O at 22.2 GHz (4 epochs), CH3OH at 6.7 GHz (3 epochs), and OH at 1.665 GHz (1 epoch). In addition, we performed high-resolution (> 0".1), high-sensitivity (< 0.1 mJy) VLA observations of the radio continuum emission from the HMC at 1.3 and 3.6 cm. Results: We have detected H2O, CH3OH, and OH maser emission clustered within 2000 AU from the center of a flattened HMC, oriented SE-NW, from which emerges a massive 12CO outflow, elongated NE-SW, extended up to the pc-scale. Although the three maser species show a clearly different spatial and velocity distribution and sample distinct environments around the massive YSO, the spatial symmetry and velocity field of each maser specie can be explained in terms of expansion from a common center, which possibly denotes the position of the YSO driving the maser motion. Water masers trace both a fast shock (up to 50 km/s) closer to the YSO, powered by a wide-angle wind, and a slower (20 km/s) bipolar jet, at the base of the large-scale outflow. Since the compact free-free emission is found offset from the putative location of the YSO along a direction consistent with that of the maser jet axis, we interpret the radio continuum in terms of a thermal jet. The velocity field of methanol masers can be explained in terms of a composition of slow (4 km/s in amplitude) motions of radial expansion and rotation about an axis approximately parallel to the maser jet. Finally, the distribution of line of sight velocities of the hydroxyl masers suggests that they can trace gas less dense (n(H2) < 10^6 cm^-3) and more distant from the YSO than that traced by the water and methanol masers, which is expanding toward the observer. (Abridged)
We generalize the coalescing Brownian flow, aka the Brownian web, considered as a weak flow to allow varying drift and diffusivity in the constituent diffusion processes and call these flows coalescing diffusive flows. We then identify the time-reversal of each coalescing diffusive flow and provide two distinct proofs of this identification. One of which is direct and the other proceeds by generalizing the concept of a localized disturbance flow to allow varying size and shape of disturbances, we show these new flows converge weakly under appropriate conditions to a coalescing diffusive flow and identify their time-reversals.
This is a survey written for the Proceedings of the AMS Summer Institute in Algebraic Geometry held in Seattle in 2005. Topics discussed in the survey include the ample and the effective cone of the moduli space of curves, Kodaira dimension, Slope Conjecture, log canonical models etc.
In [1], Weinberg made a conjecture about the little-group representations of massless particles that can be created out of the vacuum by the action of a local operator in $d$ dimensions, generalizing his old result [2] in $d=4$. In this note, I prove his conjecture and extend it to arbitrary irreps of $so(1,d-1)$.
We have studied the temperature-pressure phase diagram of CeCoSi by electrical-resistivity experiments under pressure. Our measurements revealed a very unusual phase diagram. While at low pressures no dramatic changes and only a slight shift of the Ne\'{e}l temperature $T_N$ ($\approx 10$ K) are observed, at about 1.45 GPa a sharp and large anomaly, indicative of the opening of a spin-density-wave (SDW) gap, appears at a comparatively high temperature $T_S \approx 38$ K. With further increasing pressure $T_S$ shifts rapidly to low temperatures and disappears at about 2.15 GPa, likely continuously in a quantum critical point, but without evidence for superconductivity. Even more surprisingly, we observed a clear shift of $T_S$ to higher temperatures upon applying a magnetic field. We discuss two possible origins for $T_S$, either magnetic ordering of Co or a meta-orbital type of transition of Ce.
We use gradient Young measures generated by Lipschitz maps to define a relaxation of integral functionals which are allowed to attain the value $+\infty$ and can model ideal locking in elasticity as defined by Prager in 1957. Furthermore, we show the existence of minimizers for variational problems for elastic materials with energy densities that can be expressed in terms of a function being continuous in the deformation gradient and convex in the gradient of the cofactor (and possibly also the gradient of the determinant) of the corresponding deformation gradient. We call the related energy functional gradient polyconvex. Thus, instead of considering second derivatives of the deformation gradient as in second-grade materials, only a weaker higher integrability is imposed. Although the second-order gradient of the deformation is not included in our model, gradient polyconvex functionals allow for an implicit uniform positive lower bound on the determinant of the deformation gradient on the closure of the domain representing the elastic body. Consequently, the material does not allow for extreme local compression.
We calculate the Landau interaction function f(k,k') for the two-dimensional t-t' Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface.
We consider real random walks with finite variance. We prove an optimal integrability result for the diffusively rescaled maximum, when the walk or its bridge is conditioned to stay positive, or to avoid zero. As an application, we prove tightness under diffusive rescaling for general pinning and wetting models based on random walks.
The energy per particle, symmetry energy, pressure, Free energy are calculated for asymmetric nuclear matter using BHF approach and modern nucleon-nucleon CD-Bonn, Nijm1, Argonnev18 and Reid93 potentials. To obtain saturation in nuclear matter we add three-body interaction terms which are equivalent a la Skyrme to a density-dependent two-nucleon interaction. Good agreement is obtained in comparison with previous theoretical estimates and experimental data.
We use Keck laser guide star adaptive optics imaging and exploit the magnifying effects of strong gravitational lensing (the effective resolution is FWHM ~ 200 pc) to investigate the sub-kpc scale of an intermediate-redshift (z = 0.63) massive early-type galaxy being lensed by a foreground early-type galaxy; we dub this class of strong gravitational lens systems EELs, e.g., early-type/early-type lenses. We find that the background source is massive (M* = 10^{10.9} M_sun) and compact (r_e = 1.1 kpc), and a two-component fit is required to model accurately the surface brightness distribution, including an extended low-surface-brightness component. This extended component may arise from the evolution of higher-redshift `red nuggets' or may already be in place at z ~ 2 but is unobservable due to cosmological surface brightness dimming.
We use a density-functional based tight-binding method to study diamond growth steps by depositing dicarbon species onto a hydrogen-free diamond (110) surface. Subsequent C_2 molecules are deposited on an initially clean surface, in the vicinity of a growing adsorbate cluster, and finally, near vacancies just before completion of a full new monolayer. The preferred growth stages arise from C_2n clusters in near ideal lattice positions forming zigzag chains running along the [-110] direction parallel to the surface. The adsorption energies are consistently exothermic by 8--10 eV per C_2, depending on the size of the cluster. The deposition barriers for these processes are in the range of 0.0--0.6 eV. For deposition sites above C_2n clusters the adsorption energies are smaller by 3 eV, but diffusion to more stable positions is feasible. We also perform simulations of the diffusion of C_2 molecules on the surface in the vicinity of existing adsorbate clusters using an augmented Lagrangian penalty method. We find migration barriers in excess of 3 eV on the clean surface, and 0.6--1.0 eV on top of graphene-like adsorbates. The barrier heights and pathways indicate that the growth from gaseous dicarbons proceeds either by direct adsorption onto clean sites or after migration on top of the existing C_2n chains.
We derive the the effective lagrangian that describes the interactions among vector, axial-vector mesons and pseudoscalars starting from the extended chiral quark model (ECQM). The results for the low-energy constants of this effective lagrangian have a parametric resemblance with existing predictions based on the Nambu-Jona-Lasinio model (except for some overall signs that we correct), but are numerically different. Therefore a precise measurement of these decay constants can shed some light on the way chiral symmetry breaking is modelled in QCD. Although most of the constants are poorly measured, comparison with phenomenology allows us to determine one of the parameters of the ECQM that could not be fully determined in previous analyses.
We give a simple necessary and sufficient condition for uniform K-stability of $\mathbb{Q}$-Fano varieties.
We present a method to estimate the lensing potential from massive galaxy clusters for given observational X-ray data. The concepts developed and applied in this work can easily be combined with other techniques to infer the lensing potential, e.g. weak gravitational lensing or galaxy kinematics, to obtain an overall best fit model for the lensing potential. After elaborating on the physical details and assumptions the method is based on, we explain how the numerical algorithm itself is implemented with a Richardson-Lucy algorithm as a central part. Our reconstruction method is tested on simulated galaxy clusters with a spherically symmetric NFW density profile filled with gas in hydrostatic equilibrium. We describe in detail how these simulated observational data sets are created and how they need to be fed into our algorithm. We test the robustness of the algorithm against small parameter changes and estimate the quality of the reconstructed lensing potentials. As it turns out we achieve a very high degree of accuracy in reconstructing the lensing potential. The statistical errors remain below 2.0% whereas the systematical error does not exceed 1.0%.
To understand the stellar population content of dwarf early-type galaxies (dEs) and its environmental dependence, we compare the slopes and intrinsic scatter of color-magnitude relations (CMRs) for three nearby clusters, Fornax, Virgo and Coma. Additionally we present and compare internal color profiles of these galaxies to identify central blue regions with younger stars.   We use the imaging of the HST/ACS Fornax cluster in the magnitude range of -18.7 <= M_g' <= -16.0, to derive magnitudes, colors and color profiles, which we compare with literature measurements.   Based on analysis of the color profiles, we report a large number of dEs with young stellar populations in their center in all three clusters. While for Virgo and Coma the number of blue-cored dEs is found to be 85 +/- 2% and 53 +/- 3% respectively, for Fornax, we find that all galaxies have a blue core. We show that bluer cores reside in fainter dEs, similar to the trend seen in nucleated dEs. We find no correlation between the luminosity of the galaxy and the size of its blue core. Moreover, a comparison of the CMRs of the three clusters shows that the scatter in Virgo's CMR is considerably larger than in the Fornax and Coma clusters. Presenting adaptive smoothing we show that the galaxies on the blue side of the CMR often show evidence for dust extinction, which strengthens the interpretation that the bluer colors are due to young stellar populations. We also find that outliers on the red side of the CMR are more compact than expected for their luminosity. We find several of these red outliers in Virgo, often close to more massive galaxies. No red outlying compact early-types are found in Fornax and Coma in this magnitude range while we find three in the Virgo cluster. We suggest that the large number of outliers and larger scatter found for the Virgo cluster CMR is a result of Virgo's different assembly history.
We present subarcsecond images of submillimeter CO and continuum emission from a local galaxy forming massive star clusters: the blue compact dwarf galaxy II Zw 40. At $\sim$0.4" resolution (20 pc), the CO(3-2), CO(1-0), 3mm and 870${\mu}$m continuum maps illustrate star formation on the scales of individual molecular clouds. Dust contributes about a third of the 870${\mu}$m continuum emission, with free-free accounting for the rest. On these scales, there is not a good correspondence between gas, dust, and free-free emission. Dust continuum is enhanced toward the star-forming region as compared to the CO emission. We suggest that an unexpectedly low and spatially variable gas-to-dust ratio is the result of massive clusters of the starburst.
The present notes are the expanded and polished version of three lectures given in Stanford, concerning the analytic and arithmetic properties of weight one modular forms. The author tried to write them in a style accessible to non-analytically oriented number theoritists: in particular, some effort is made to be precise on statements involving uniformity in the parameters. On the other hand, another purpose was to provide an introduction, together with a set of references, consciously kept small, to the realm of Galois representations, for non-algebraists -- like the author. The proofs are sketched, at best, but we tried to motivate the results, and to relate them to interesting conjectures.
In this paper, we consider isotropic and stationary real Gaussian random fields defined on $\mathbb{S}^2\times\mathbb{R}$ and we investigate the asymptotic behavior, as $T\rightarrow +\infty$, of the empirical measure (excursion area) in $\mathbb{S}^2\times\mathbb{R}$ at any threshold, covering both cases when the field exhibits short and long memory, i.e. integrable and non-integrable temporal covariance. It turns out that the limiting distribution is not universal, depending both on the memory parameters and the threshold. In particular, in the long memory case a form of Berry's cancellation phenomenon occurs at zero-level, inducing phase transitions for both variance rates and limiting laws.
In this paper we apply techniques of spherical harmonic analysis to prove a local limit theorem, a rate of escape theorem, and a central limit theorem for isotropic random walks on arbitrary thick regular affine buildings of irreducible type.