ShantanuT01/DACTYL-Pretraining huggingface dataset:
Recent results concerning solutions of the modified Helmholtz equation are reviewed; namely, various mean value properties and their corollaries, converse and inverse of these properties, and relations between these solutions and harmonic functions.
This paper has been withdrawn by the author. The most updated version can be accessed by arXiv:1806.07290.
A typical sunspot, as seen in white-light intensity images, has a two part structure: a dark umbra and a lighter penumbra. Such distinction primarily arises due to the different orientations of magnetic fields in these two regions. In this study, we use the Kodaikanal white-light digitized data archive to analyze the long-term evolution of umbral and penumbal area. We developed an 'automated algorithm' to uniquely identify the sunspot umbra (including the calculation of penumbra to umbra ratio) from these digitized intensity images. Our analysis reveals that the ratio increases slightly with the increase of sunspot area upto 100 msh but eventually settles down to a constant value after that.This study, not only allows us to better understand the evolution of an individual spot and its corresponding magnetic field but this is also beneficial for solar dynamo studies which aim to reproduce such structures using a MHD theory.
Echo mapping exploits light travel time delays, revealed by multi-wavelength variability studies, to map the geometry, kinematics, and physical conditions of reprocessing sites in photo-ionized gas flows. In AGNs, the ultra-violet to near infra-red light arises in part from reprocessing of EUV and X-ray light from a compact and erratically variable source in the nucleus. The observed time delays, 0.1-2 days for the continuum, 1-100 days for the broad emission lines, probe regions only micro-arcseconds away from the nucleus. The continuum time delays map the temperature-radius profiles of the AGN accretion discs. The emission-line delays reveal radially stratified ionization zones, identify the nature of the gas motions, and estimate the masses of the central black holes. By using light travel time to measure the sizes of AGN accretion discs and photo-ionized zones, echo mapping offers two independent ways to measure redshift-independent distances to AGNs.
Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The distinctive scaling properties of the model at criticality, however, strongly suggest that it should belong to a different universality class than ordinary percolation. Here we introduce a generalization of the product rule that reveals the effect of non-locality on the critical behavior of the percolation process. Precisely, pairs of unoccupied bonds are chosen according to a probability that decays as a power-law of their Manhattan distance, and only that bond connecting clusters whose product of their sizes is the smallest, becomes occupied. Interestingly, our results for two-dimensional lattices at criticality shows that the power-law exponent of the product rule has a significant influence on the finite-size scaling exponents for the spanning cluster, the conducting backbone, and the cutting bonds of the system. In all three cases, we observe a continuous variation from ordinary to (non-local) explosive percolation exponents.
We discuss recent advances in the study of dusty, massive galaxies at z>1 arising from the first extensive spectroscopic surveys.
In this paper, we examine the emergence of conserved charges on the horizon of a particular class of extremal non-dilatonic black $p$-branes (which reduce to extremal dilatonic black holes in $D=4$ dimensions upon toroidal compactification) in the presence of a probe massless scalar field in the bulk. This result is achieved by writing the black $p$-brane geometry in a Gaussian null coordinate system which allows us to get a non-singular near-horizon geometry description. We find that the near-horizon geometry is $AdS_{p+2}\times S^2$ and that the $AdS_{p+2}$ section has an internal structure which can be seen as a warped product of $AdS_{2}\times S^{p}$ in Gaussian null coordinates. We show that the bulk scalar field satisfying the field equations is expanded in terms of non-normalizable and normalizable modes, which for certain suitable quantization conditions are well-behaved at the boundary of $AdS_{p+2}$ space. Furthermore, we show that picking the normalizable modes results in the existence of conserved quantities on the horizon. We discuss the impact of these conserved quantities in the late time regime.
The method of QCD light-cone sum rules is used to calculate soft nonfactorizable contributions to the decay amplitude for B -> J/psi K. The result confirms expectations that in color-suppressed decays nonfactorizable corrections can be sizable.
We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply this result to various quantities arising in stochastic geometry, including: size of the largest component for percolation on a box; number of components, number of edges, or number of isolated points, for random geometric graphs; covered volume for germ-grain coverage models; number of accepted points for finite-input random sequential adsorption; sum of nearest-neighbour distances for a random sample from a continuous multidimensional distribution.
We provide a consistent description of the kinetic equation with triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for minimum number of unknown coefficients in one charge and two charge cases by solving the constraining equations.
A triple system is cancellative if no three of its distinct edges satisfy $A \cup B=A \cup C$. It is tripartite if it has a vertex partition into three parts such that every edge has exactly one point in each part. It is easy to see that every tripartite triple system is cancellative. We prove that almost all cancellative triple systems with vertex set [n] are tripartite. This sharpens a theorem of Nagle and Rodl on the number of cancellative triple systems. It also extends recent work of Person and Schacht who proved a similar result for triple systems without the Fano configuration. Our proof uses the hypergraph regularity lemma of Frankl and Rodl, and a stability theorem for cancellative triple systems due to Keevash and the second author.
Euler showed that the number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts. This theorem was generalized by Glaisher and further by Franklin. Recently, Beck made three conjectures on partitions with restricted parts, which were confirmed analytically by Andrews and Chern and combinatorially by Yang.   Analogous to Euler's partition theorem, it is known that the number of compositions of $n$ with odd parts equals the number of compositions of $n+1$ with parts greater than one, as both numbers equal the Fibonacci number $F_n$. Recently, Sills provided a bijective proof for this result using binary sequences, and Munagi proved a generalization similar to Glaisher's result using the zigzag graphs of compositions. Extending Sills' bijection, we obtain a further generalizaiton which is analogous to Franklin's result. We establish, both analytically and combinatorially, two closed formulas for the number of compositions with restricted parts appearing in our generalization. We also prove some composition analogues for the conjectures of Beck.
How to prepare deterministically non-Gaussian entangled states is a fundamental question for continuous-variable quantum information technology. Here, we theoretically demonstrate through numerical methods that the triple-photon state generated by three-photon spontaneous parametric down-conversion is a pure super-Gaussian resource of non-Gaussian entanglement. Interestingly, the degree of entanglement between the modes of the triple-photon state is stronger than that corresponding to the two-mode squeezed vacuum state produced by a quadratic Hamiltonian with the same parameters. Furthermore, we propose a model to prepare two-mode non-Gaussian entangled states with tunable non-Gaussianity based on quadrature projection measurements.
In this paper we establish all extremal graphs with respect to augmented eccentric connectivity index among all (simple connected) graphs, among trees and among trees with perfect matching. For graphs that turn out to be extremal explicit formulas for the value of augmented eccentric connectivity index are derived.
This year the discovery of femtosecond demagnetization by laser pulses is 20 years old. For the first time this milestone work by Bigot and coworkers gave insight in a very direct way into the time scales of microscopic interactions that connect the spin and electron system. While intense discussions in the field were fueled by the complexity of the processes in the past, it now became evident that it is a puzzle of many different parts. Rather than giving an overview that has been presented in previous reviews on ultrafast processes in ferromagnets, this perspective will show that with our current depth of knowledge the first real applications are on their way: THz spintronics and all-optical spin manipulation are becoming more and more feasible. The aim of this perspective is to point out where we can connect the different puzzle pieces of understanding gathered over 20 years to develop novel applications. based on many observations in a large number of experiments. Differences in the theoretical models arise from the localized and delocalized nature of ferromagnetism. Transport effects are intrinsically non-local in spintronic devices and at interfaces. We review the need for multiscale modeling to address processes starting from electronic excitation of the spin system on the picometer length scale and sub-femtosecond time scale, to spin wave generation, and towards the modeling of ultrafast phase transitions that altogether determine the response time of the ferromagnetic system. Today, our current understanding gives rise to the first real applications of ultrafast spin physics for ultrafast magnetism control: THz spintronic devices. This makes the field of ultrafast spin-dynamics an emerging topic open for many researchers right now.
We systematically investigated the temperature behaviors of the electrical conductivity and Hall coefficient of two series of amorphous indium gallium zinc oxides (a-IGZO) films prepared by rf sputtering method. The two series of films are $\sim$700\,nm and $\sim$25\,nm thick, respectively. For each film, the conductivity increases with decreasing temperature from 300\,K to $T_{\rm max}$, where $T_{\rm max}$ is the temperature at which the conductivity reaches its maximum. Below $T_{\rm max}$, the conductivity decreases with decreasing temperature. Both the conductivity and Hall coefficient vary linearly with $\ln T$ at low temperature regime. The $\ln T$ behaviors of conductivity and Hall coefficient cannot be explained by the traditional electron-electron interaction theory, but can be quantitatively described by the current electron-electron theory due to the presence of granularity. Combining with the scanning electron microscopy images of the films, we propose that the boundaries between the neighboring a-IGZO particles could make the film inhomogeneous and play an important role in the electron transport processes.
Consider the edge-deletion process in which the edges of some finite tree T are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this edge-deletion process. Our main result shows that after a proper rescaling, the cut-tree of a critical Galton-Watson tree with finite variance and conditioned to have size n, converges as $n\to\infty$ to a Brownian continuum random tree (CRT) in the weak sense induced by the Gromov-Prokhorov topology. This yields a multi-dimensional extension of a limit theorem due to Janson [Random Structures Algorithms 29 (2006) 139-179] for the number of random cuts needed to isolate the root in Galton-Watson trees conditioned by their sizes, and also generalizes a recent result [Ann. Inst. Henri Poincar\'{e} Probab. Stat. (2012) 48 909-921] obtained in the special case of Cayley trees.
To leading order in $\alpha_s$, we evaluate the leading and non-leading $1/M_b$ corrections to the $B^*B\pi$ and $B^*B\gamma$ couplings using QCD spectral moment sum rules in the full theory. We find that, for large $M_b$ and contrary to the heavy-to-light $B\rar \pi(\rho) l\bar \nu$ form factors, which are dominated by the $soft$ light quark vacuum condensate, these couplings are governed by the $hard$ perturbative graph, like other heavy-to-heavy transitions. We also find that for the $B^{*}\rar B\gamma$, the $1/M_b$ correction is mainly due to the perturbative and light quark condensate contributions originating from the graphs involving the heavy quark part of the electromagnetic current, which are essential for explaining the large charge dependence in the observed $D^{*-}\rar D^-\gamma$ and $D^{*0}\rar D^0\gamma$ decays. Our $best$ numerical predictions {\it without any free parameters} for the $B^*$-meson are: $g_{B^{*-}B^0\pi^-}\simeq 14\pm 4$, $\Gamma_{B^{*-}\rar B^-\gamma}\simeq (0.10\pm 0.03)$ keV and the large charge dependence of the ratio: ${\Gamma_{B^{*-}\rar B^- \gamma}}/ {\Gamma_{B^{*0}\rar B^0 \gamma}}\simeq 2.5~$. For the $D^*$-meson, we find: $\Gamma_{D^{*-}\rar D^0\pi^-}\simeq 1.54\Gamma_{D^{*0}\rar D^0\pi^0} \simeq (8\pm 5)$ keV, $\Gamma_{D^{*-}\rar D^-\gamma}\simeq (0.09^{+0.40}_{-0.07} )$ keV and $\Gamma_{D^{*0}\rar D^0\gamma}\simeq (3.7\pm 1.2)$ keV, where the branching ratios agree within the errors with the present data, while the total widths $\Gamma_{D^{*0}\rar all} \simeq (11\pm 4)$ keV and $\Gamma_{D^{*-}\rar all}\simeq (12\pm 7)$ keV are much smaller than the present experimental upper limits.
Our first result is that a homogeneous form $F$ in $n$ variables is GIT semistable with respect to the natural $SL(n)$-action if and only if the first non-trivial Hilbert point of the associated Milnor algebra is semistable. We also prove that the induced morphism on the GIT quotients is finite, and injective on the locus of stable forms. Our second result is that the associated form of $F$, also known as the Macaulay inverse system of the Milnor algebra of $F$, and which is apolar to the last non-trivial Hilbert point of the Milnor algebra, is GIT semistable whenever $F$ is a smooth form. These two results answer questions of Alper and Isaev from arXiv:1407.6838.
Observations of pulsar glitches have the potential to provide constraints on the dynamics of the high density interior of neutron stars. However, to do so, realistic glitch models must be constructed and compared to the data. We take a step towards this goal by testing non-linear models for the mutual friction force, which is responsible for the exchange of angular momentum between the neutron superfluid and the observable normal component in a glitch. In particular, we consider a non-linear dependence of the drag force on the relative velocity between superfluid vortices and the normal component, in which the contributions of both kelvon and phonon excitations are included. This non-linear model produces qualitatively new features, and is able to reproduce the observed bimodal distribution of glitch sizes in the pulsar population. The model also suggests that the differences in size distributions in individual pulsars may be due to the glitches being triggered in regions with different pinning strengths, as stronger pinning leads to higher vortex velocities and a qualitatively different mutual friction coupling with respect to the weak pinning case. Glitches in pulsars that appear to glitch quasi-periodically with similar sizes may thus be due to the same mechanisms as smaller events in pulsars that have no preferred glitch size, but simply originate in stronger pinning regions, possibly in the core of the star.
Consider on a manifold the solution $X$ of a stochastic differential equation driven by a L\'evy process without Brownian part. Sufficient conditions for the smoothness of the law of $X_t$ are given, with particular emphasis on noncompact manifolds. The result is deduced from the case of affine spaces by means of a localisation technique. The particular cases of Lie groups and homogeneous spaces are discussed.
We present preliminary results from the recent multi-epoch HI absorption measurements toward several pulsars using the Arecibo telescope. We do not find significant variations in optical depth profiles over periods of 4 months and 9 years. The upper limits on the optical depth variations in directions of B0823+26 and B1133+16 are similar on scales of 10--20, 350 and 500 AU. The large number of non detections of the tiny scale atomic structure suggests that the AU-sized structure is not ubiquitous in the interstellar medium.
We perform extensive Monte Carlo simulations of a two-dimensional bent hard-needle model in both its chiral zig-zag and its achiral bow-shape configurations and present their phase diagrams. We find evidence for a variety of stable phases: isotropic, quasi-nematic, smectic-C, anti-ferromorphic smectic-A, and modulated-nematic. This last phase consists of layers formed by supramolecular arches. They create a periodic modulation of the molecular polarity whose period is sensitively controlled by molecular geometry. We identify transition densities using correlation functions together with appropriately defined order parameters and compare them with predictions from Onsager theory. The contribution of the molecular excluded area to deviations from Onsager theory and simple liquid crystal phase morphology is discussed. We demonstrate the isotropic--quasi-nematic transition to be consistent with a Kosterlitz-Thouless disclination unbinding scenario.
Liquids and solids are two fundamental states of matter. However, due to the lack of direct experimental determination, our understanding of the 3D atomic structure of liquids and amorphous solids remained speculative. Here we advance atomic electron tomography to determine for the first time the 3D atomic positions in monatomic amorphous materials, including a Ta thin film and two Pd nanoparticles. We observe that pentagonal bipyramids are the most abundant atomic motifs in these amorphous materials. Instead of forming icosahedra, the majority of pentagonal bipyramids arrange into networks that extend to medium-range scale. Molecular dynamic simulations further reveal that pentagonal bipyramid networks are prevalent in monatomic amorphous liquids, which rapidly grow in size and form icosahedra during the quench from the liquid state to glass state. The experimental method and results are expected to advance the study of the amorphous-crystalline phase transition and glass transition at the single-atom level.
Chiral multifold fermions are quasiparticles described by higher spin generalizations of the Weyl equation, and are realized as low energy excitations near symmetry protected band crossings in certain chiral crystals. In this work we calculate the linear optical conductivity of all chiral multifold fermions. We show that it is enhanced with respect to that of Weyl fermions with the same Fermi velocity, and features characteristic activation frequencies for each multifold fermion class, providing an experimental fingerprint to detect them. We calculate the conductivity for realistic chiral multifold semimetals by using lattice tight-binding Hamiltonians that match the effective models of multifold fermions at low energies, for space groups 199 and 198. The latter includes RhSi, for which we give quantitative predictions, and also CoSi and AlPt. Our predictions can be tested in absorption or penetration depth measurements, and are necessary to extract the recently proposed quantized photocurrents from experiments.
The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The supersymmetric version is also studied and more precisely in the case of the Schwinger model on supersphere [14]. This paper is a generalization of this latter work to more general gauge groups.
In a 1916 paper, Ramanujan studied the additive convolution $S_{a, b}(n)$ of sum-of-divisors functions $\sigma_a(n)$ and $\sigma_b(n)$, and proved an asymptotic formula for it when $a$ and $b$ are positive odd integers. He also conjectured that his asymptotic formula should hold for all positive real $a$ and $b$. Ramanujan's conjecture was subsequently proved by Ingham, and then by Halberstam with a power saving error term.   In this paper, we give a new proof of Ramanujan's conjecture that obtains lower order terms in the asymptotics for most ranges of the parameters. We also describe a connection to a counting problem in geometric topology that was studied in the second author's thesis and which served as our initial motivation in studying this sum.
A variety of analytical techniques suggest that quantum fluctuations lead to a fundamental instability of the Fermi liquid that drives ferromagnetic transitions first order at low temperatures. We present both analytical and numerical evidence that, driven by the same quantum fluctuations, this first order transition is pre-empted by the formation of an inhomogeneous magnetic phase. This occurs in a manner that is closely analogous to the formation of the inhomogeneous superconducting Fulde-Ferrel-Larkin-Ovchinnikov state. We derive these results from a field theoretical approach supplemented with numerical Quantum Monte Carlo simulations. Our analytical approach represents a considerable simplification over diagrammatic methods, makes contact with older analyses of the unitarity limit, and enables a simple physical picture to emerge.
Using exact numerical techniques we investigate the nature of excitonic (electron-hole) bound states and the development of exciton coherence in the one-dimensional half-filled extended Falicov-Kimball model. The ground-state phase diagram of the model exhibits, besides band insulator and staggered orbital ordered phases, an excitonic insulator (EI) with power-law correlations. The criticality of the EI state shows up in the von Neumann entropy. The anomalous spectral function and condensation amplitude provide the binding energy and coherence length of the electron-hole pairs which, on their part, point towards a Coulomb interaction driven crossover from BCS-like electron-hole pairing fluctuations to tightly bound excitons. We show that while a mass imbalance between electrons and holes does not affect the location of the BCS-BEC crossover regime it favors staggered orbital ordering to the disadvantage of the EI. Within the BEC regime the quasiparticle dispersion develops a flat valence-band top in accord with the experimental finding for Ta$_2$NiSe$_5$.