ShantanuT01/DACTYL-Pretraining huggingface dataset:
Percolation for a planar lattice has a single percolation threshold, whereas percolation for a negatively curved lattice displays two separate thresholds. The enhanced binary tree (EBT) can be viewed as a prototype model displaying two separate percolation thresholds. We present an analytic result for the EBT model which gives two critical percolation threshold probabilities, $p_{c1}=1/2\sqrt{13}-3/2$ and $p_{c2}=1/2$, and yields a size-scaling exponent $\Phi =\ln [\frac{p(1+p)}{1-p(1-p)}]/\ln 2$. It is inferred that the two threshold values give exact upper limits and that $p_{c1}$ is furthermore exact. In addition, we argue that $p_{c2}$ is also exact. The physics of the model and the results are described within the midpoint-percolation concept: Monte Carlo simulations are presented for the number of boundary points which are reached from the midpoint, and the results are compared to the number of routes from the midpoint to the boundary given by the analytic solution. These comparisons provide a more precise physical picture of what happens at the transitions. Finally, the results are compared to related works, in particular, the Cayley tree and Monte Carlo results for hyperbolic lattices as well as earlier results for the EBT model. It disproves a conjecture that the EBT has an exact relation to the thresholds of its dual lattice.
Let $K$ be a global function field and fix a place $\infty$ of $K$. Let $L/K$ be a finite real abelian extension, i.e. a finite, abelian extension such that $\infty$ splits completely in $L$. Then we define a group of elliptic units $C_L$ in $\mathcal{O}_L^\times$ analogously to Sinnott's cyclotomic units and compute the index $[\mathcal{O}_L^\times:C_L]$. In the second part of this article, we additionally assume that $L$ is a cyclic extension of prime power degree. Then we can use the methods from Greither and Ku\v{c}era to take certain roots of these elliptic units and prove a result on the annihilation of the $p$-part of the class group of $L$.
We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal universe. We show that the mass corresponds to values obtained previously for quark stars when anisotropy and charge are present.
We give a strong version of a classic inequality of \L ojasiewicz; one which collapses to the usual inequality in the complex analytic case. We show that this inequality for a pair, quadruple, or octuple of real analytic functions allows us to construct a real Milnor fibration inside a ball.
A number of authors have studied the question of when a graph can be represented as a Cayley graph on more than one nonisomorphic group. The work to date has focussed on a few special situations: when the groups are $p$-groups; when the groups have order $pq$; when the Cayley graphs are normal; or when the groups are both abelian. In this paper, we construct two infinite families of graphs, each of which is Cayley on an abelian group and a nonabelian group. These families include the smallest examples of such graphs that had not appeared in other results.
There is strong observational evidence that many active galactic nuclei (AGNs) harbour supermassive black holes (SMBHs), demonstrating multi-accretion episodes during their lifetime. In such AGNs, corotating and counterrotating tori, or strongly misaligned disks, as related to the central SMBH spin, can report traces of the AGNs evolution. Here we concentrate on aggregates of accretion disks structures, ringed accretion disks (RADs) orbiting a central Kerr SMBH, assuming that each torus of the RADs is centered in the equatorial plane of the BH, tori are coplanar and axisymmetric. Many RAD aspects are governed mostly by the Kerr geometry spin. We classify Kerr BHs due to their dimensionless spin, according to possible combinations of corotating and counterrotating equilibrium or accreting tori composing the RADs. The number of accreting tori in RADs cannot exceed n=2. We present list of 14 characteristic values of the BH spin a governing the classification in the BH range 0<a<M, constrained by the RAD properties. The spins are remarkably close providing an accurate characterization of the Kerr BHs based on the RAD properties. RAD dynamics is richer in the spacetimes of high spins. One of the critical predictions states that a RAD tori couple formed by an outer accreting corotating and an inner accreting counterrotating torus is expected to be observed only around slowly spinning (a<0.46M) BHs. The analysis strongly binds the fluid and BH characteristics providing indications on the situations where to search for RADs observational evidences. Obscuring and screening tori, possibly evident as traces in Xray spectrum emission, are strongly constrained, eventually ruling out many assumptions used in the current investigations of the screening effects. We expect relevance of our classification of Kerr BHs in relation to AGNs phenomena that could be observed by the Xray satellite ATHENA.
This is a review of theoretical attempts to describe production of heavy quark bound states in nucleus-nucleus collisions, in particular, the relative suppression of $J/\psi$ and $\psi'$ production observed in these reactions. The review begins with a survey of experimental data for proton-induced reactions and their theoretical interpretation. The evidence for additional suppression in nucleus-nucleus collisions is discussed and various theoretical models of charmonium absorption by comoving matter are presented and analyzed. The review concludes with suggestions for future research that would help clarify the implications of $J/\psi$ suppression in Pb + Pb collisions observed by the NA50 experiment.
In an attempt to bridge the gap between atomistic and continuum plasticity simulations of hydrogen in iron, we present three dimensional discrete dislocation plasticity simulations incorporating the hydrogen elastic stress and a hydrogen dependent dislocation mobility law. The hydrogen induced stress is incorporated following the formulation derived by Gu and El-Awady (2018) which here we extend to a finite boundary value problem, a microcantilever beam, via the superposition principle. The hydrogen dependent mobility law is based on first principle calculations by Katzarov et al. (2017) and was found to promote dislocation generation and enhance slip planarity at a bulk hydrogen concentration of 0.1 appm; which is typical for bcc materials. The hydrogen elastic stress produced the same behaviour, but only when the bulk concentration was extremely high. In a microcantilever, hydrogen was found to promote dislocation activity which lowered the flow stress and generated more pronounced slip steps on the free surfaces. These observations are consistent with the hydrogen enhanced localized plasticity (HELP) mechanism, and it is concluded that both the hydrogen elastic stress and hydrogen increased dislocation mobility are viable explanations for HELP. However it is the latter that dominates at the low concentrations typically found in bcc metals.
Motivated by the recent discovery of the binary neutron-star (BNS) merger GW170817, we determine the optimal observational setup for detecting and characterizing radio counterparts of nearby ($d_L\sim40$\,Mpc) BNS mergers. We simulate GW170817-like radio transients, and radio afterglows generated by fast jets with isotropic energy $E_{\rm iso}\sim 10^{50}$\,erg, expanding in a low-density interstellar medium (ISM; $n_{\rm ISM}=10^{-4}-10^{-2}$\,cm$^{-3}$), observed from different viewing angles (from slightly off-axis to largely off-axis). We then determine the optimal timing of GHz radio observations following the precise localization of the BNS radio counterpart candidate, assuming a sensitivity comparable to that of the Karl G. Jansky Very Large Array. The optimization is done so as to ensure that properties such as viewing angle and circumstellar density can be correctly reconstructed with the minimum number of observations. We show that radio is the optimal band to explore the fastest ejecta from BNSs in low-density ISM, since the optical emission is likelyto be dominated by the so-called `kilonova' component, while X-rays from the jet are detectable only for a small subset of the BNS models considered here. Finally, we discuss how future radio arrays like the next generation VLA (ngVLA) would improve the detectability of BNS mergers with physical parameters similar to the ones here explored.
We consider one-dimensional excited random walks with finitely many cookies at each site. There are certain natural monotonicity results that are known for the excited random walk under some partial orderings of the cookie environments. We improve these monotonicity results to be strictly monotone under a partial ordering of cookie environments introduced by Holmes and Salisbury. While the self-interacting nature of the excited random walk makes a direct coupling proof difficult, we show that there is a very natural coupling of the associated branching process from which the monotonicity results follow.
We give the classification of 3-dimensional Bol algebras associated to the trilinears operations $(e_2,e_3, e_2)=e_1, (e_2, e_3, e_3)=\pme_2$. It turn that for such trilinears operation there exist up to isomorphism and isotopy one family and one exceptional Bol algebras. We describe their corresponding 3-webs.
By using the work of Frantzikinakis and Wierdl, we can see that for all $d\in\mathbb{N}$, $\alpha\in(d,d+1)$, and integers $k\ge d+2$ and $r\ge1$, there exist infinitely many $n\in\mathbb{N}$ such that the sequence $(\lfloor{(n+rj)^\alpha}\rfloor)_{j=0}^{k-1}$ is represented as $\lfloor{(n+rj)^\alpha}\rfloor=p(j)$, $j=0,1,\ldots,k-1$, by using some polynomial $p(x)\in\mathbb{Q}[x]$ of degree at most $d$. In particular, the above sequence is an arithmetic progression when $d=1$. In this paper, we show the asymptotic density of such numbers $n$ as above. When $d=1$, the asymptotic density is equal to $1/(k-1)$. Although the common difference $r$ is arbitrarily fixed in the above result, we also examine the case when $r$ is not fixed. Most results in this paper are generalized by using functions belonging to Hardy fields.
Some considerations showing that renormalizable theories with consistent perturbative theries can not be nonperturbatively finite (in terms of bare parameters) are provided. Accordingly any fundamental unified theory has to be either non renormalizable or order by order finite.
This paper introduces an order proximity on a collection of objects induced by a partial order using the Smirnov closeness measure on a Sz\'{a}z relator space. A Sz\'{a}z relator is a nonempty family of relations defined on a nonvoid set $K$. The Smirnov closeness measure provides a straightforward means of assembling partial ordered of pairwise close sets. In its original form, Ju. M. Smirnov closeness measure $\delta(A,B) = 0$ for a pair of nonempty sets $A,B$ with nonvoid intersection and $\delta(A,B) = 1$ for non-close sets. A main result in this paper is that the graph obtained by the proximity is equivalent to the Hasse diagram of the order relation that induces it. This paper also includes an application of order proximity in detecting sequences of video frames that have order proximity.
We report an unexpected characteristic of dislocation cores in silicon. Using first-principles calculations, we show that all the stable core configurations for a non-dissociated 60$^\circ$ dislocation are sessile. The only glissile configuration, previously obtained by nucleation from surfaces, surprinsingly corresponds to an unstable core. As a result, the 60$^\circ$ dislocation motion is solely driven by stress, with no thermal activation. We predict that this original feature could be relevant in situations for which large stresses occur, such as mechanical deformation at room temperature. Our work also suggests that post-mortem observations of stable dislocations could be misleading, and that mobile unstable dislocation cores should be taken into account in theoretical investigations.
Del Pezzo surfaces over C with log terminal singularities of index \le 2 were classified by Alekseev and Nikulin. In this paper, for each of these surfaces, we find an appropriate morphism to projective space. These morphisms enable us to describe del Pezzo surfaces of index \le 2 by equations in some weighted projective space. Obtained results are natural completions of similar results of Du Val, and Hidaka and Watanabe, describing del Pezzo surfaces of index 1.
We study a one-dimensional totally asymmetric simple exclusion process with one special site from which particles fly to any empty site (not just to the neighboring site). The system attains a non-trivial stationary state with density profile varying over the spatial extent of the system. The density profile undergoes a non-equilibrium phase transition when the average density passes through the critical value 1-1/[4(1-ln 2)]=0.185277..., viz. in addition to the discontinuity in the vicinity of the special site, a shock wave is formed in the bulk of the system when the density exceeds the critical density.
This article summarizes some physics aspects of the market model of Weisbuch and Stauffer, Physica A (2003): How do demand and quality expectation adjust to each other in a buyer dominated market like cinema visits? And how can business cycles be modelled?
One fundamental challenge in building an instance segmentation model for a large number of classes in complex scenes is the lack of training examples, especially for rare objects. In this paper, we explore the possibility to increase the training examples without laborious data collection and annotation. We find that an abundance of instance segments can potentially be obtained freely from object-centric images, according to two insights: (i) an object-centric image usually contains one salient object in a simple background; (ii) objects from the same class often share similar appearances or similar contrasts to the background. Motivated by these insights, we propose a simple and scalable framework FreeSeg for extracting and leveraging these "free" object foreground segments to facilitate model training in long-tailed instance segmentation. Concretely, we investigate the similarity among object-centric images of the same class to propose candidate segments of foreground instances, followed by a novel ranking of segment quality. The resulting high-quality object segments can then be used to augment the existing long-tailed datasets, e.g., by copying and pasting the segments onto the original training images. Extensive experiments show that FreeSeg yields substantial improvements on top of strong baselines and achieves state-of-the-art accuracy for segmenting rare object categories.
In this paper, the Buckley-Feuring method (BFM) and the variational iteration method (VIM) are used for find exact fuzzy solution of the fuzzy heat-like equations in one and two dimensions. Several examples are given to show the new theorem of Buckley-Feuring solution and the Seikkala solution. The results obtained in all cases show the reliability and the efficiency of this methods.
General-relativistic simulations of binary neutron star mergers with viscosity reveal a new outflow mechanism operating in unequal mass binaries on dynamical timescales and enabled by turbulent viscosity. These "viscous-dynamical" ejecta are launched during merger due to the thermalization of mass exchange streams between the secondary and the primary neutron star. They are characterized by asymptotic velocities extending up to ${\sim} 0.8\, c$, and have masses that depend on the efficiency of the viscous mechanism. Depending on the unknown strength of the effective viscosity arising from magnetohydrodynamics instabilities operating during merger, the overall mass of the dynamical ejecta could be enhanced by a factor of a few and the mass of the fast tail of the ejecta having asymptotic velocities $\geq 0.6\, c$ by up to four orders of magnitude. The radioactive decay of the expanding viscous-dynamical ejecta could produce bright kilonova transients with signatures of free neutron decay in the first hour and enhanced near infrared flux on a timescale of a few days. The synchrotron remnant produced by the interaction between the ejecta and the interstellar medium could also be significantly enhanced by viscosity. Such remnant could be detected in the case of GW170817 as a rebrightening of the radio signal in the next months to years.
The surface mass density of a cluster of galaxies, and thus its total mass, can be estimated from its lens magnification. The magnification can be determined from the variation in number counts of its background galaxies. In the weak lensing approximation the surface mass density is a linear function of the magnification. However, most observational data is concentrated in the central parts of clusters, so one needs to go beyond the weak lensing approximation, and consider the lens shear as well, which is unknown from the variation in number counts alone. We studied the lensing properties of a catalogue of numerical cluster models in order to find the best possible approximation for the shear which still allows straightforward determination of the surface mass density. We show that by using such an approximation one can fairly well reconstruct the surface mass distribution from the magnification alone. It is demonstrated that the mass estimated using the weak lens magnification approximation is usually at least twice the true mass. We illustrate our technique on existing data, and show that the resulting masses compare well to other estimates.
In a preceding paper [E.J.ofProb.34,860-892,(2006)], we proved a sewing lemma which was a key result for the study of Holder continuous functions. In this paper we give a non-commutative version of this lemma with some applications.
We report the statistics of the number of active regions (NAR) observed at 17 GHz with the Nobeyama Radioheliograph between 1992, near the maximum of cycle 22, and 2013, that also includes the maximum of cycle 24, and we compare with other activity indexes. We find that NAR minima are shorter than those of the sunspot number (SSN) and radio flux at 10.7 cm (F10.7). This shorter NAR minima could reflect the presence of active regions generated by faint magnetic fields or spotless regions, which were a considerable fraction of the counted active regions. The ratio between the solar radio indexes F10.7/NAR shows a similar reduction during the two minima analyzed, which contrasts with the increase of the ratio of both radio indexes in relation to the SSN during the minimum of cycle 23-24. These results indicate that the radio indexes are more sensitive to weaker magnetic fields than those necessary to form sunspots, of the order of 1500 G. The analysis of the monthly averages of the active region brightness temperatures shows that its long term variation mimics the solar cycle, although, due to the gyro-resonance emission, a great number of intense spikes are observed in the maximum temperature study. The decrease, in number, of these spikes is also evident during the current cycle 24, a consequence of the sunspot magnetic field weakening in the last years.
The importance of accurate simulation of the plastic deformation of ductile metals to the design of structures and components is well-known. Many techniques exist that address the length scales relevant to deformation pro- cesses, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dis- locations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focused on the system-level material response that use DD-generated information to enhance the fidelity of plasticity models. To ascertain to what degree the predictions of CP are consistent with those of DD, we compare their global and microstructural response in a number of deformation modes. After using nominally homogeneous compression and shear deformation dislocation dynamics simulations to calibrate crystal plasticity flow rule parameters, we compare not only the system-level stress-strain response of prismatic wires in torsion but also the resulting geometrically necessary dislocation density fields. To establish a connection between explicit description of dislocations and the continuum assumed with crystal plasticity simulations, we ascertain the minimum length-scale at which meaningful dislocation density fields appear. Our results show that, for the case of torsion, the two material models can produce comparable spatial dislocation density distributions.
Observation of non-zero neutrino masses at a scale $\sim 10^{-1} - 10^{-2}$ eV is a major problem in the otherwise highly successful Standard Model. The most elegant mechanism to explain such tiny neutrino masses is the seesaw mechanism with right handed neutrinos. However, the required seesaw scale is so high, $\sim 10^{14}$ GeV, it will not have any collider implications. Recently, an explicit model has been constructed to realize the seesaw mechanism with the right handed neutrinos at the electroweak scale. The model has a mirror symmetry having both the left and right lepton and quark doublets and singlets for the same $SU(2)_W $ gauge symmetry. Additional Higgs multiplets have been introduced to realize this scenario. It turns out that these extra Higgs fields also help to satisfy the precision electroweak tests, and other observables. Because the scale of the symmetry breaking is electroweak, both the mirror quark and mirror leptons have masses in the electroweak scale in the range $ \sim 150 - 800 $ GeV. The mirror quarks / leptons decay to ordinary quarks /leptons plus very light neutral scalars. In this work, we calculate the final state signals arising from the pair productions of these mirror quarks and their subsequent decays. We find that these signals are well observable over the Standard Model background for $13$ TeV LHC. Depending on the associated Yukawa couplings, these decays can also give rise displaced vertices with long decay length, very different from the usual displaced vertices associated with b decays.
We study the symmetric Anderson-Holstein (AH) model at zero temperature with Wilson's numerical renormalization group (NRG) technique to study the interplay between the electron-electron and electron-phonon interactions. An improved method for calculating the phonon propagator using the NRG technique is presented, which turns out to be more accurate and reliable than the previous works in that it calculates the phonon renormalization explicitly and satisfies the boson sum rule better. The method is applied to calculate the renormalized phonon propagators along with the electron propagators as the onsite Coulomb repulsion $U$ and electron-phonon coupling constant $g$ are varied. As $g$ is increased, the phonon mode is successively renormalized, and for $g \gtrsim g_{co}$ crosses over to the regime where the mode splits into two components, one of which approaches back to the bare frequency and the other develops into a soft mode. The initial renormalization of the phonon mode, as $g$ is increased from 0, depends on $U$ and the hybridization $\Delta$; it gets softened (hardened) for $U \gtrsim (\lesssim) U_s (\Delta)$. Correlated with the emergence of the soft mode is the central peak of the electron spectral function severely suppressed. These NRG calculations will be compared with the standard Green's function results for the weak coupling regime to understand the phonon renormalization and soft mode.