ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that every bounded subset of an Euclidean space can be approximated by a set that admits a certain vector field, the so-called Cahn-Hoffman vector field, that is subordinate to a given anisotropic metric and has a square-integrable divergence. More generally, we introduce a concept of facets as a kind of directed sets, and show that they can be approximated in a similar manner.   We use this approximation to construct test functions necessary to prove the comparison principle for viscosity solutions of the level set formulation of the crystalline mean curvature flow that were recently introduced by the authors. As a consequence, we obtain the well-posedness of the viscosity solutions in an arbitrary dimension, which extends the validity of the result in the previous paper.
Formulation of the Penrose inequality becomes ambiguous when the past and future apparent horizons do cross. We test numerically several natural possibilities of stating the inequality in punctured and boosted single- and double- black holes, in a Dain-Friedrich class of initial data and in conformally flat spheroidal data.The Penrose inequality holds true in vacuum configurations for the outermost element amongst the set of disjoint future and past apparent horizons (as expected)and (unexpectedly) for each of the outermost past and future apparent horizons, whenever these two bifurcate from an outermost minimal surface, regardless of whether they intersect or remain disjoint. In systems with matter the conjecture breaks down only if matter does not obey the dominant energy condition.
Gravitational lensing can provide pure geometric tests of the structure of space-time, for instance by determining empirically the angular diameter distance-redshift relation. This geometric test has been demonstrated several times using massive clusters which produce a large lensing signal. In this case, matter at a single redshift dominates the lensing signal, so the analysis is straightforward. It is less clear how weaker signals from multiple sources at different redshifts can be stacked to demonstrate the geometric dependence. We introduce a simple measure of relative shear which for flat cosmologies separates the effect of lens and source positions into multiplicative terms, allowing signals from many different source-lens pairs to be combined. Applying this technique to a sample of groups and low-mass clusters in the COSMOS survey, we detect a clear variation of shear with distance behind the lens. This represents the first detection of the geometric effect using weak lensing by multiple, low-mass systems. The variation of distance with redshift is measured with sufficient precision to constrain the equation of state of the universe under the assumption of flatness, equivalent to a detection of a dark energy component Omega_X at greater than 99% confidence for an equation-of-state parameter -2.5 < w < -0.1. For the case w = -1, we find a value for the cosmological constant density parameter Omega_Lambda = 0.85+0.044-0.19 (68% C.L.), and detect cosmic acceleration (q_0 < 0) at the 98% C.L.. We consider the systematic uncertainties associated with this technique and discuss the prospects for applying it in forthcoming weak-lensing surveys.
We investigate the possible signature of the presence of giant pairing states at excitation energy of about 10 MeV via two-particle transfer reactions induced by neutron-rich weakly-bound projectiles. Performing particle-particle RPA calculations on $^{208}$Pb and BCS+RPA calculations on $^{116}$Sn, we obtain the pairing strength distribution for two particles addition and removal modes. Estimates of two-particle transfer cross sections can be obtained in the framework of the 'macroscopic model'. The weak-binding nature of the projectile kinematically favours transitions to high-lying states. In the case of $(~^6He, \~^4He)$ reaction we predict a population of the Giant Pairing Vibration with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state.
The present paper is devoted to the construction of a catalog of isolated galaxy pairs from the Uppsala Galaxy Catalog (UGC), using accurate radial velocities. The UGC lists 12921 galaxies to declination larger than -2 deg 30 min and is complete to an apparent diameter of 1 arcmin. The criteria used to define the isolated galaxy pairs are the following: 1) Velocity criterion: radial velocity difference between the members lower than 500 km/s; 2) Interdistance criterion: projected distance between the members smaller than 1 Mpc; 3) Reciprocity criterion: each member is the closest galaxy to the other one, which excludes multiplets; 4) Isolation information: the catalog lists the ratio between the projected distance to the closest UGC galaxy (having a velocity difference smaller than 500 km/s) and the pair members interdistance, thus allowing one to choose any isolation criterion (beyond the chosen limit 2.5). In addition, we have accounted for the small diameter bias by searching for CGCG galaxies in the pair environment and used the same isolation criterion. A peculiar investigation has allowed to gather very accurate radial velocities for pair members, from high quality HI and optical measurements (median uncertainty on velocity differences 10 km/s). Our final catalog contains 1005 galaxy pairs. Then we give some global properties of the pair catalog. We display the histograms of the radial velocity differences between the pair members and of their projected interdistances (median 0.29 Mpc). Finally, we provide an estimate of the contamination by cosmological false "pairs", which is about 10 percent up to a velocity difference of 380 km/s, beyond which all pairs are probably false.
The Binder cumulant (BC) has been widely used for locating the phase transition point accurately in systems with thermal noise. In systems with quenched disorder, the BC may show subtle finite-size effects due to large sample-to-sample fluctuations. We study the globally coupled Kuramoto model of interacting limit-cycle oscillators with random natural frequencies and find an anomalous dip in the BC near the transition. We show that the dip is related to non-self-averageness of the order parameter at the transition. Alternative definitions of the BC, which do not show any anomalous behavior regardless of the existence of non-self-averageness, are proposed.
We consider a non reactive multi component gas mixture.We propose a class of models, which can be easily generalized to multiple species. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the solutions for the space homogeneous case, positivity of all temperatures, H-theorem and convergence to a global equilibrium in the space homogeneous case in the form of a global Maxwell distribution. Thus, we are able to derive the usual macroscopic conservation laws. In particular, by considering a mixture composed of ions and electrons, we derive the macroscopic equations of ideal MHD from our model.
We analyze the electrostatic self-energy of a point like electrically charged particle induced by a cosmic string in the context of gravity's rainbow, as well the electrostatic self-force on this particle. The possibility of the solution associated with a charged particle to be altered by modifications in dispersion relations of the space-time is discussed. We show that the self-energy depends on the rainbow functions and that this quantity can either increase or decrease depending on the rainbow function chosen, as compared with analogous result in the framework of general relativity. With respect to the self-force, its dependence with the rainbow functions is also pointed out
The behavior at criticality of spatial SIR (susceptible/infected/recovered) epidemic models in dimensions two and three is investigated. In these models, finite populations of size N are situated at the vertices of the integer lattice, and infectious contacts are limited to individuals at the same or at neighboring sites. Susceptible individuals, once infected, remain contagious for one unit of time and then recover, after which they are immune to further infection. It is shown that the measure-valued processes associated with these epidemics, suitably scaled, converge, in the large-N limit, either to a standard Dawson-Watanabe process (super-Brownian motion) or to a Dawson-Watanabe process with location-dependent killing, depending on the size of the the initially infected set. A key element of the argument is a proof of Adler's 1993 conjecture that the local time processes associated with branching random walks converge to the local time density process associated with the limiting super-Brownian motion.
Time-dependent calculation has been a suitable method to investigate the quantum dynamical processes. In Ref. [1] = [T. Oishi et al., J. of Phys. G 45, 105101 (2018)], we applied this method to the one-dimensional two-fermion tunneling in the nuclear-physics scale. Beside the specific results presented therein, some basic formalism and methods, which can be helpful for further discussions and developments to investigate time-dependent quantum systems, have been awaiting our description. This note is devoted to describe those supplemental contents. We do not limit the story to the nuclear physics, but keep it applicable to other scales and/or targets.
Quasi-biennial oscillations (QBOs) are considered as a fundamental mode of solar magnetic activity at low latitudes ($\leq50^\circ$). However, the evolutionary aspect and the hemispheric distribution of solar QBOs at high latitudes ($\geq60^\circ$) are rarely studied. Here, a relatively novel time-frequency analysis technique, named the synchrosqueezed wavelet transform, is applied to extract the main components of the polar faculae in the northern and southern hemispheres for the time interval from August 1951 to December 1998. It is found as the following: (1) Apart from the 22-year Hale cycle, the 17-year extended activity cycle, and the 11-year Schwabe cycle, the QBOs have been estimated as a prominent timescale of solar magnetic activity at high latitudes; (2) the QBOs of the polar faculae are coherent in the two hemispheres, but the temporal (phase) and the spatial (amplitude) variations of solar QBOs occur unevenly on both hemispheres; and (3) for the 11-year period mode, the northern hemisphere begins three months earlier than that in the southern one. Moreover, the spatial and temporal distributions of the hemispheric QBOs differ from those of the 11-year Schwabe cycle mode in the two hemispheres. Our findings could be helpful to improve our knowledge on the physical origin of the spatial distribution of solar QBOs at high latitudes, and could also provide more constraints on solar dynamo models introduced to characterize the different components of the solar magnetic activity cycle.
Consider the process which starts with $N\ge 3$ distinct points on ${\mathbb R}^d$, and fix a positive integer~$K<N$. Of the total $N$ points keep those $N-K$ which minimize the energy (defined as the sum of all pairwise distances squared) amongst all the possible subsets of size $N-K$, and then replace the removed points by $K$ i.i.d.\ points sampled according to some fixed distribution $\zeta$. Repeat this process ad infinitum. We obtain various quite non-restrictive conditions under which the set of points converges to a certain limit. This is a very substantial generalization of the "Keynesian beauty contest process" studied by Grinfeld, Volkov and Wade, where $K=1$ and the distribution $\zeta$ was uniform on the unit cube.
The structural and vibrational properties of metal-organic interfaces have been examined by means of infrared (IR) absorption spectroscopy and density functional theory (DFT) with an approach accounting for long-range dispersive interactions. We focus on a comparative study of the PTCDA monolayer and bilayer on Ag(111). The equilibrium geometry at the molecule-metal interface and the infrared spectrum of the chemisorbed monolayer of PTCDA on Ag(111) are well described by the computations. In the bilayer structure, the presence of a physisorbed adlayer on top of PTCDA/Ag(111) presents a challenge for DFT. As previously described for other systems, the polarization of the substrate is not captured correctly and results in too low energies of frontier molecular orbitals. This results in an apparent contribution from the vibrations of second-layer PTCDA to the IR spectrum from interfacial dynamical charge transfer processes. After removing these peaks with artificially strong intensity, calculated and experimental data show good agreement and the IR spectrum can be described as the sum of the spectra of the PTCDA/Ag(111) contact layer and a physisorbed PTCDA monolayer on top.
We use a recently developed extension of the weak coupling diagrammatic determinantal quantum Monte Carlo method to investigate the spin, charge and single particle spectral functions of the one-dimensional quarter-filled Holstein model with phonon frequency $\omega_0 = 0.1 t$. As a function of the dimensionless electron-phonon coupling we observe a transition from a Luttinger to a Luther-Emery liquid with dominant $2k_f$ charge fluctuations. Emphasis is placed on the temperature dependence of the single particle spectral function. At high temperatures and in both phases it is well accounted for within a self-consistent Born approximation. In the low temperature Luttinger liquid phase we observe features which compare favorably with a bosonization approach retaining only forward scattering. In the Luther-Emery phase, the spectral function at low temperatures shows a quasiparticle gap which matches half the spin gap whereas at temperatures above which this quasiparticle gap closes, characteristic features of the Luttinger liquid model are apparent. Our results are based on lattice simulations on chains up to L=20 for two-particle properties and on CDMFT calculations with clusters up to 12 sites for the single-particle spectral function.
For any graph, we define a rank-1 operator on a bipartite tensor product space, with components associated to the set of vertices and edges respectively. We show that the partial traces of the operator are the Laplacian and the edge-Laplacian. This provides an interpretation of the von Neumann entropy of the (normalized)\ Laplacian as the amount of quantum entanglement between two systems corresponding to vertices and edges. In this framework, cospectral graphs correspond exactly to local unitarily equivalent pure states. Finally, we introduce the notion of coentropic graphs, that is, graphs with equal von Neumann entropy. The smallest coentropic (but not cospectral) graphs that we are able to construct have 8 vertices. The number of equivalence classes of coentropic graphs with n vertices and m edges is a lower bound to the number of (pure) bipartite entanglement classes with subsystems of corresponding dimension.
We present ground-based 3 micron spectra of obscured Asymptotic Giant Branch (AGB) stars in the Magellanic Clouds (MCs). We identify the carbon stars on the basis of the 3.1 micron absorption by HCN and C2H2 molecules.   We show evidence for the existence of carbon stars up to the highest AGB luminosities (Mbol=-7 mag, for a distance modulus to the LMC of 18.7 mag). This proves that Hot Bottom Burning (HBB) cannot, in itself, prevent massive AGB stars from becoming carbon star before leaving the AGB. It also sets an upper limit to the distance modulus of the Large Magellanic Cloud of 18.8 mag.   The equivalent width of the absorption band decreases with redder (K-L) colour when the dust continuum emission becomes stronger than the photospheric emission. Carbon stars with similar (K-L) appear to have equally strong 3 micron absorption in the MCs and the Milky Way. We discuss the implications for the carbon and nitrogen enrichment of the stellar photosphere of carbon stars.
Ferromagnetic transitions between quantum Hall states with different polarization at a fixed filling factor can be studied by varying the ratio of cyclotron and Zeeman energies in tilted magnetic field experiments. However, an ability to locally control such transitions at a fixed magnetic field would open a range of attractive applications, e.g. formation of a reconfigurable network of one-dimensional helical domain walls in a two-dimensional plane. Coupled to a superconductor, such domain walls can support non-Abelian excitation. In this article we report development of heterostructures where quantum Hall ferromagnetic (QHFm) transition can be controlled locally by electrostatic gating. A high mobility two-dimensional electron gas is formed in CdTe quantum wells with engineered placement of paramagnetic Mn impurities. Gate-induced electrostatic field shifts electron wavefunction in the growth direction and changes overlap between electrons in the quantum well and d-shell electrons on Mn, thus controlling the s-d exchange interaction and the field of the QHFm transition. The demonstrated shift of the QHFm transition at a filling factor $\nu=2$ is large enough to allow full control of spin polarization at a fixed magnetic field.
Gaze estimation involves predicting where the person is looking at within an image or video. Technically, the gaze information can be inferred from two different magnification levels: face orientation and eye orientation. The inference is not always feasible for gaze estimation in the wild, given the lack of clear eye patches in conditions like extreme left/right gazes or occlusions. In this work, we design a model that mimics humans' ability to estimate the gaze by aggregating from focused looks, each at a different magnification level of the face area. The model avoids the need to extract clear eye patches and at the same time addresses another important issue of face-scale variation for gaze estimation in the wild. We further extend the model to handle the challenging task of 360-degree gaze estimation by encoding the backward gazes in the polar representation along with a robust averaging scheme. Experiment results on the ETH-XGaze dataset, which does not contain scale-varying faces, demonstrate the model's effectiveness to assimilate information from multiple scales. For other benchmark datasets with many scale-varying faces (Gaze360 and RT-GENE), the proposed model achieves state-of-the-art performance for gaze estimation when using either images or videos. Our code and pretrained models can be accessed at https://github.com/ashesh-0/MultiZoomGaze.
From measurements of the far-infrared reflectivity at grazing angles of incidence with p-polarized light we determined the c-axis Josephson plasma frequencies of the single layer high T_c cuprates Tl_2Ba_2CuO_6 and La_{2-x}Sr_xCuO_4. We detected a strong plasma resonance at 50 cm^{-1} for La_{2-x}Sr_xCuO_4 in excellent agreement with previously published results. For Tl_2Ba_2CuO_6 we were able to determine an upper limit of the unscreened c-axis Josephson plasma frequency 100 cm^{-1} or a c-axis penetration depth > 15 \mu m. The small value of $\omega_J$ stands in contrast to recent a prediction based on the inter-layer tunneling mechanism of superconductivity.
We discuss D-brane monodromies from the point of view of the gauged linear sigma model. We give a prescription on how to extract monodromy matrices directly from the hemisphere partition function. We illustrate this procedure by recomputing the monodromy matrices associated to one-parameter Calabi-Yau hypersurfaces in weighted projected space.
Assuming $B_{R}$ is a ball in $\mathbb R^{N}$, we analyze the positive solutions of the problem \[   \begin{cases}   -\Delta u+u= |u|^{p-2}u, &\text{ in } B_{R},\newline   \partial_{\nu}u=0,&\text{ on } \partial B_{R},   \end{cases}   \] that branch out from the constant solution $u=1$ as $p$ grows from $2$ to $+\infty$. The non-zero constant positive solution is the unique positive solution for $p$ close to $2$. We show that there exist arbitrarily many positive solutions as $p\to\infty$ (in particular, for supercritical exponents) or as $R \to \infty$ for any fixed value of $p>2$, answering partially a conjecture in [Bonheure-Noris-Weth]. We give the explicit lower bounds for $p$ and $R$ so that a given number of solutions exist. The geometrical properties of those solutions are studied and illustrated numerically. Our simulations motivate additional conjectures. The structure of the least energy solutions (among all or only among radial solutions) and other related problems are also discussed.
We show that the coherent oscillations of the e.m. field induced by the collective quantum fluctuations of the nuclear matter field associated with the giant resonances, with frequencies $\omega_{A}\simeq 78A^{-{1/3}}$ MeV, give rise to a significant $(e^+e^-)$ pair production in high energy Heavy Ion collisions. The approximate parameterless calculation of such yield is in good agreement with recent experimental observations.
We revisit the problem of the helicity-0 ghost mode of massive graviton in the de Sitter background. In general, the presence of a ghost particle, which has negative energy, drives the vacuum to be unstable through pair production of ghost particles and ordinary particles. In the case that the vacuum state preserves the de Sitter invariance, the number density created by the pair production inevitably diverges due to unsuppressed ultra-violet(UV) contributions. In such cases one can immediately conclude that the model is not viable. However, in the massive gravity theory we cannot construct a vacuum state which respects the de Sitter invariance. Therefore the presence of a ghost does not immediately mean the breakdown of the model. Explicitly estimating the number density and the energy density of particles created by the pair production of two conformal scalar particles and one helicity-0 ghost graviton, we find that these densities both diverge. However, since models with helicity-0 ghost graviton have no de Sitter invariant vacuum state, it is rather natural to consider a UV cutoff scale in the three-dimensional momentum space. Then, even if we take the cutoff scale as large as the Planck scale, the created number density and energy density are well suppressed. In many models the cutoff scale is smaller than the Planck scale. In such models the created number density and the energy density are negligiblly small as long as only the physics below the cutoff scale is concerned.
Measurements of neutron total cross-sections are both extensive and extremely accurate. Although they place a strong constraint on theoretically constructed models, there are relatively few comparisons of predictions with experiment. The total cross-sections for neutron scattering from $^{16}$O and $^{40}$Ca are calculated as a function of energy from $50-700$~MeV laboratory energy with a microscopic first order optical potential derived within the framework of the Watson expansion. Although these results are already in qualitative agreement with the data, the inclusion of medium corrections to the propagator is essential to correctly predict the energy dependence given by the experiment.
In this work we study Podolsky electromagnetism in thermodynamic equilibrium. We show that a Podolsky mass-dependent modification to the Stefan-Boltzmann law is induced and we use experimental data to limit the possible values for this free parameter.